You camping? Florida Keys! Has city buses from Homestead, FL to Key West, jump off where ever there's a stop. Yosemite NP, that's more of a visit though. How you traveling? Bicycle? Car? Try the West Coast. Washington state to Malibu, CA. The Coast area you can actually travel by public transportation a huge amount of the way. 2 or 3 spot you have to make your own way for 30-40 mile. Gaberville, Ca area and King City, Ca area. Camping alone the West Coast has plenty of State, county and National Park. Cheap camping $5- 410 a night. People are just fine and plenty safe.
Just about anywhere is fine to travel on your own. I would never let being on my own stop me from taking an interesting trip. When you travel solo, you get to see and do the things that most interest you. You can spend as much or as little time as you want in a given activity. You also have the flexibility to change plans on the fly if you run across an interesting festival, exhibition, concert or other event.
You can almost travel and stay overnight in a hotel/motel. Call ahead to be sure they will take you; they may not. Because of your age.
Yellowstone Park AMAZING