It depends a lot on what exactly you mean by "around there". While there are no real mountains in the immediate area around Prague, you can find a number of great places to hike there. If you a willing to go a bit further, you can find some nice mountains, too. Also, I am not sure if by two day hike you mean a backpacking trip with sleeping outdoors, or if you plan to find some other means of accomodation.
I can give you some information that is based on my own experience from over 20 years ago, together with chats with friends and information availabe on the web.
First, two useful pieces of information everyone looking for hiking or backpacking opportunities in Czech Republic:
The country is crisscrossed by an extensive system of inteconnected hiking trails, that allows you to get on foot from pretty much any place to any other place. The system is maintained by the Klub Českých Turistů (Czech Tourist Club), and consists of two components: trail markings and corresponding maps. Each trail is assigned one of four colors: red, yellow, green or blue. It used to be that red color was reserved for long distance trails, often following a long mountain range or a similar such feature, yellow trails were shorter, branching from the red ones, and green and blue were reserved for local or connecting trails, but as far as I can tell, that is no longer strictly followed.
The trails are marked in terain by trail marks that look like a horizontal color stripe (red, yellow, green or blue) between two horizontal white stripes, like this:
They are usually found on trees, rocks or buildings, and can look like this.
At places where the trail changes direction, it is often marked using an arrow version of the mark:
There are several other variations, marking a spring or well, historic ruin, vista point etc. Intersections of trails usually have pointers telling you what direction to take to get to various locations, as well as their distances in kilometers.
The other component of the trail system is a collection of maps, that have the color coded trails mark in them. They are usually quite detailed and easy to use. You can buy them in any bookstore, newspaper stand, and in many museum and souvenir shops. The online map server at mapy.cz has a setting that shows the trails as well.
The second thing is of interest to backpackers. While it is illegal to "wild camp" in Czech Republic, in most areas it is a fairly common practice. If one is smart about it, one can usually avoid detection, and even when discovered, if you clearly behave well, do not damage the environment, do not litter etc, and behave politely, forest or park rangers often let you go. There is some dispute about it, but it seems that it is actually legal to sleep in the woods as long as you do not make a fire and do not build any kind of shelter. There are number of exceptions, mainly in national parks and nature preserves, but in general, you can sleep in woods if you do it in a smart way.
Now, back to hiking opportunities near Prague. There are actually several shorter but nice hikes. One of them is the "Prokopské valley". You can either take a bus to the Zlíchov station and take the blue trail up to the valley, or, from Jinonice subway station, yellow and green trails both go down. The valley has a number of interesting geological features. Other interesting areas are "Modřanská rokle" on the other side of the river, area around Roztoky and Suchdol in the north, the Botič valley in the east, and several other smaller areas. These are all shorter hikes, partly through urban or suburban environment, but can be quite nice.
For longer hikes, and more natural ones, I recommend the region in the south of Prague. It is more hilly, with some prety good hiking.
Probably the most mountain like part of this region is the area called Brdy. It is a range of wooded hills that stretch from the southern edge of Prague for some 50 or 60 km south west past Příbram. Unfortunately the central part of this range belongs to the military and is mostly closed to the public, but the northern part has some very nice hiking. There are several ways how to get there from Prague:
- The main red trail starts at what I remember used to be a small insignificant city bus stop at Zbraslav-Báně. From there it continues the entire length of the "northern" Brdy. I highly recommend to follow it all the way to the Plešivec mountain. It would make a good long one day hike. If you want to continue for two days, there are number of places to camp for the night in that area. If you are lucky, you may even find a place with a makeshift shelter and a fireplace. If you do, please treat it gently. There is a tradition in this region to very carefully clean the fireplace when you are leaving, and to leave a small fir branch pointing in the direction in which you left in the middle of it. If zou want to return back to Prague, you can walk down to Hostomice, Jince or another small town and take a local train to Zadní Třebáň, where you switch to the main line and return to Prague. You can also continue further, with several option, perhaps following yellow and green trail further south west. It skirts the military zone, entering it at several places that are open to public, and follows all the way to the town of Rokycany. Another option is to partially backtrack, return to Dobříš, and follow for example the blue trail to the Vltava valley, which has plenty of local hiking opportunities, and generally good transportation back to Prague.
- Instead of trying to find the red trail in Zbraslav, you can take a train from the Smichov train station to either of Dobřichovice, Mokropsy or Všenory. From any of those stations, you can take a blue trail that will take you up the hill to the main red one. You can also take a bus to Jíloviště, the bus stop should be on or near the main red trail.
- Finally, you can take a train from the Bráník train station to Dobříš, and enter Brdy from that direction.
To get some idea what you can see in Brdy, you can look at this site.
Another great area for hiking, less hilly but perhaps more interesting, is just on the other side of the Berounka river. The "Český Kras" (Bohemian Karst) is somewhat more popular and can be, at least in some areas, quite crowded, but if you avaid the most obvious tourist attractions, you can find some excellent hinkng.
Again, there is a number of ways how to get there:
- For the longest hike, you can actually continue the Prokopske Valley hike described above. From the central part of the valley, you take a blue trail to Slivenec. In Slivenec you switch to the red trail, and take it to Kalinův Mlýn, where you switch to a blue trail again. (You can also get to Kalinův Mlýn from the upper end of the Prokopske Valley, if you take a blue trail from there. From Kalinův Mlýn, you follow the blue trail pretty much south to Kulivá Hora, where you switch to a red trail towards Karlštejn.
- Another option is to take a train from the Smíchov station to Radotín (you shold also be able to get there by a city bus). In Radotín, you can get directly onto the red trail towards Karlštejn.
- You can also stay on the train for a little longer, get off in Černošice and take a green or blue trail from there. Both of them will eventually meet the red trail to Karlštejn.
You will then follow the red trail through Karlík valley and Mořinka all the way to Karlštejn. The castle in Karlštejn is a very popular tourist attraction, and can be pretty crowded. Most visitors take a train or bus to the village, and climb the souvenir shop encrusted road up to the castle. The red trail will bring you to the castle from different side. You will still have to pass through some of the madness, but you will avoid the worst. You can visit the castle if you want. Then continue on the red trail past the castle. Keep following the red trail till you get to an intersection of several trails called "Propadlé Vody". From there you have number of options, but my favorite always was to take the yellow trail to the north, marked on the map as "Svatojánský okruh" (St. John circle). It will take you past the Arnika cave, through some interesting long abandoned limestone quarries all the way to a vist point on the top of the cliff overlooking the St. John valley and the monastery. Bacrtacking a bit and following the trail further will take you down to the valley.
From there, you have several options. You can take the blue trail north and catch a train or bus in Vráž. You can stay on the red trail and end up in the city of Beroun, with several options for transportation back tp Prague. Or you can take the yellow trail south to Srbsko, where you can take a train back to Prague.
If you want to hike more, you have a number of options, including those:
- You can pass through Beroun westwards to Nižbor, where another area with numerous hiking opportunities opens: Křivoklátsko. You can spend some time there, or you can turn south through Zbiroh, and eventually end up in Brdy.
- If you end up following the yellow trail to Srbsko, instead of getting on a train, you can cross the river and the train tracks, and follow the yellow trail throu th ebeautiful Koda valley, then to Koněprusy, where you can visit some very nice and quite famous caves. You can then follow the yellow trail to the Popovice train station, or turn south, and by a combination of marked trails and roads get to Brdy.
Finally, my third suggestion is the Sázava river valley. Take a train from the Bráník train station to Pikovice, take a red trail, cross the river and follow it upstream (again, depending on how much time you have, you may want to start closer to Prague, or even in Prague. You can catch the same red trail in Zbraslav or Vrané. In fact, it is just a different part of the same red trail that leads through Karlštejn.) The trail will closely follow the Sázava river, with a nice view of its rapids. You can follow it all the way to Kamený Přívoz, where it will cross the river again. There you will have several options. You can take a train back to Prague, follow a series of green, blue, red and yellow trails back to Pikovice or even to Prague, or continue on the red trail to Prosečnice. From there you can take the yellow trail through Vlčí Rokle (the Wolf Ravine), which is quite interesting and nice. After that you will have a whole scale of possibilities, there are number of trails that you can take, most of them leading you eventually to a train or bus station.
Hopefully this will be at least somewhat helpful. Enjoy your visit. Perhaps one more advice: Czechs are generally rather fond of hiking, and many of them know their hiking areas quite well. If you are going there for a conference, for business, of to visit friends, you may want to ask your hosts where to hike. They will probably be able to give you a better, more current advice, and perhaps they will even go with you.