I live about 35 miles northwest of Boston, so I can answer this.
The first thing you should do is join the Boston Chapter of the Appalachian Mountian Club (AMC). Once you are a member, you will have access to the extensive list of hikes they run. There will be a bunch in the White Mountains of NH, but also many shorter but closer local hikes in areas you'd probably have a hard time discovering by yourself.
As for above treeline, that's not so easy. There are a few smaller "mountains" in the area that happen to have bare tops, but that's not because the climate prohibits trees. Either enough soil hasn't formed on top since the glaciers (only 12k years ago) covered everything, or people cut them down and they haven't grown back. Mt Monadnock in southern NH (Jaffre, not quite as far as Peterborough) is bald on top, but not because it is above "tree line". Going further north there are some more bare summits, like Cardigan, but again, not because of weather prohibiting trees. The highest point in MA is Mt Greylock in the NW corner, but it is forrested on top (except for the parking lot and area around some buildings).
The closest areas to Boston that are truly above treeline are in the White Mountains. There is true alpine tundra on Franconia ridge and the higher parts of the Presidential Range. However, this area is more than 2 hours drive from Boston, although not that much more.
There is no single answer to finding places to hike. The more well known, popular, and grandiose places are well covered by the AMC maps. The White Mountain Guide Book comes with 4(?) maps that cover the White Mountain area nicely. The AT and other well known trails are there, but also many smaller less well known but very nice trails. These are all on the AMC maps. Personally, I wouldn't bother getting the guide book. You can buy the maps seperately, which is really what you want. Get the tyvek versions. They cost a little more, but really do hold up to water, abrasion, and all sorts of trail-related abuse very well. It would be worth a visit to the AMC Pinkham Notch visitor center to see what maps they have. Get your AMC membership first, which I think gives you a discount.
That was the easy part. Unlike the west and other places I've been, there are a great many smaller but still quite pretty and little used local trails. Apart from a few well known and popular areas, like the Blue Hills, Middlesex Fells, etc, there is little centralized information. Don't let that fool you though, the popular areas are only the tip of the iceberg. For example, I live in Groton, which has over 100 miles of hiking trails. You can get information about them at http://www.grotontrails.org, but if I hadn't told you, you'd probably never have found that. I am on the Trails Committee in Groton, and I like to think we do a better job than most towns around here, but all towns have some conservation land, usually with public trails.
You're not going to find alpine vistas here or 10 miles of trail without a road crossing, but there are more hidden gems than you might think. When you only have half a day and want to get out to nature, go explore some of the local places. In Groton alone we have a number of heron rookeries, numerous beaver ponds with dams and lodges, a few open vistas, swamps, meadows, pretty ponds, lots of little streams, upland woods, lots of eskers, quite a number of kettle holes, etc. Come check it out. You will likely be surprised how much nearby nature is hidden yet accessible.
One way to find the local gems is to check out some of the AMC "local walks". These are great ways to get introduced to places you would have a hard time finding on your own.