I am due to go to the States this summer (From the UK) with Camp America. After Camp (Which is in Pennsylvania) I plan to do some travelling. I finish camp on the 19th of August and will have around 3 weeks until I fly back home from New York. I would like to go to Vegas and San Francisco, then return to the east coast to see the usual places around there. A Few questions!

1) What is the best/Cheapest way to get around in the U.S
2) Is it realistic to think I will be able to Get to Vegas and San Fran and back to the east coast etc, in 3 weeks? (While allowing enough time to have a good look around?)
3) Are there cheap sort of backpacker style hostels in Big U.S Cities?

Thanks for any help!