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Many cities are a few hours (or less) drive from "nice" outdoor spaces:
90%+ of people will just drive. But driving is costly in time, money, and in other ways. For these cities how feasible and economical are carpool apps and/or public transport?
It varies a lot. You have to research each one on a case-by-case basis.
For instance San Francisco to Lake Tahoe is a variety of ski buses straight from the City, or, Amtrak's California Zephyr to Truckee then a county transit bus to the resorts. That was easy! ... Or instead of the California Zephyr, you can take the Capitols scoots to Sacramento, then another connecting bus to Truckee. On the way back, that's probably a good idea - the westbound Zephyr has already been cruising for over 50 hours from Chicago, and minor delays tend to "domino effect". So its arrival time in Truckee is highly randomized.
Conversely you have Vail, Colorado, a ski resort destination that is architected to be accessed via public transport (air).
DC to Delaware Beach is Amtrak or MARC to two city buses.
DC to Ocean City MD is ...awkward. DC to Ocean City New Jersey is a great deal easier. Get some Shriver's salt water taffy.
Moving through the rest of your list, it's all like this - either laughably easy, or miserably hard. It's hit and miss, you know.
There is no substitute for simply researching a particular case. Sometimes you get lucky, sometimes you don't, and you have to find beauty where you find it.
Perhaps this is also a bit of a European answer, but I've been known to take my bike on the train then cycle to where I'm camping (for day hikes, sea swimming, and more cycling, all with a group who drove). Last time was 30km (20 miles) from the nearest station, which is quite doable. Next time is planned to be 100km, and that might not be for everyone. Some places can take bikes by bus or coach too.
Of course it's also possible to ride all the way, but hundreds of km carrying camping and hiking gear does mean a rather laden bike, and the journey has to be thought of as part of the trip, especially if it goes over a day. I once did this when most people flew, riding 500 km over 2 days (not very successfully - I crashed badly when I was nearly there)
You can extend your range and gain flexibility by using folding bikes - these are more likely to be carried by train without advance booking, and more likely to be carried by bus. While they're not as good for carrying luggage as full-size bikes, you can ride short distances with a hiking pack.
Of course you have to consider the security of the bike at your camp, trailhead, etc. A cheap old (but well-maintained) bike locked to something solid will be OK in many places; a folding bike might be better concealed and less securely locked (but still locked to something so it doesn't look dumped). I've often left my touring bike with hiking luggage and only a weak lock to a tree for short hikes and river swims. If you have indoor accommodation booked at your destination (as I've had when the trip was mainly for day-hiking), check whether you can take the bike inside.
Public transport brings you only so far. It works for some places; for example, reaching Jasper National Park (Alberta, Canada) by train or bus is easy. Death Valley National Park (California, USA), not so much.
Where public transport ends, several alternatives exist:
Culture about hitch-hiking varies widely between countries. In the USA, the media-industrial complex has taught people to fear each other, leading to fearmongering and a consideration of hitch-hiking as extremely dangerous. I think it's actually banned in US national parks. On the other hand, it was explicitly recommended to me in Jasper National Park in Canada. The experience was not great. It took me five hours on the Icefields Parkway before a friendly singer-songwriter picked me up and brought me back to Jasper (I had not planned to hitch-hike from there, but weather forced me out of my hike early). I have successfully hitch-hiked from trailheads back to town in Canada, Iceland, Norway, Poland, France, and Sweden. It's easier if you arrive at a car park, where you can address fellow hikers directly, if there are any.
I've taken taxis to and from trailheads from the nearest public transportation. I've done this in Portugal, Spain, Switzerland, Norway, Iceland, Russia, and Canada. It costs a bit, of course, but if you are sharing with a group then the costs are manageable. Expect to pay a premium to go on a rough mountain road (although I paid the same for 120 km / 6 hours in a 6 WD including major river fords in Russia, as I did for 40 km on a major highway in Norway).
Getting to the trailhead in Yugyd Va National Park by Russian mountain taxi, fording the Ко́жим (Kozhim) river in a TREKOL, 3 September 2019.
View from inside. Note that we're in a car, not in a boat.
I've used my bicycle to get to and from trailheads, bringing all my hiking and camping gear on my trekking bike. If you can bring your bicycle on public transportation, you don't need to bike all the way from home, saving time for remote destinations. I'm considering cycling to Kverkfjöll and Nýidalur in Iceland and start hiking from there; those destinations are more than 120 km from the nearest bus stop, along rough tracks featuring unabridged river crossings; getting there by mountain taxi is out of my budget (there used to be a mountain bus, but not any more).
In Europe you can combine trains and buses. It really depends on the country, the connections are usually decent. In Italy buses during weekends can be a problem,... Most people use private transport, because if 2 or more share expenses it is way faster and cheaper. It depends how far away do you want to go. If you are out for 1-2 day tour usage of bus, train often takes too long, you need to wait for transfer,... and time is precious. If you do longer multi-day hikes and start at point A and end somewhere else - B the public transport is great. For example I don't need to do a circular route, hike from A to A. In 3 days I can walk 90-100 km and get back with public transport. It gives me much more freedom to do more interesting hikes and the ones I want.
I live in Australia, where the state of public transport is (I believe) closer to the US than to Europe.
As for public transport, it either is or isn't; you can check online. Carpool apps might work. But your best bet would be to join a hiker (or skier) online group on Facebook, Meetup, etc. Whenever people are planning a hike or another fun activity several 100 km from their city, someone usually is happy to share gas price.
Here in Austria (Linz) we’ve signed up for car sharing in order to reach cross country skiing tracks and hiking or climbing destinations. There is public transport but the bus stops or train stations are usually ≥5km away from the tracks and on weekends some connections are horrible.
The car sharing is not cheap but for a few weekends per year it’s much cheaper than owning a car. Since it’s electric cars the emissions are also somewhat okay.
