I've linked the website of Hostelling International below. Most major cities and tourist destinations have a HI hostel, and those in towns served by Amtrak are easily accessed from the station by cab, bus or foot. The majority of hostel guests do not travel by car, so it's always in a hostel's best interest to be near public transportation. Where there is none, the hostel will often pick guests up at the station or airport.
Hostels are generally clean and comfortable. The main drawback is lack of privacy. Most hostels use bunk beds, and acommodate 4-12 people per room, depending on its size. You won't exactly be crammed in, but you'll definitely be aware of other people in the room. Expect your room to be full if you're traveling during summer.
That said, I've been surprised at the level of respectfulness hostellers show one another. Theft was uncommon in the 500-bed hostel I worked at, and disputes, when they occured, were usually settled quickly and amicably. Hostels seem to promote an instant sense of community--and communal responsibility--that hotels lack. Staff, particularly in smaller hostels, are always helpful in finding restaurants and other services not provided by the hostel, as well as providing local insight on area attractions. I met many people in my time at HI who could have afforded to stay at a hotel, but chose the hostel instead for those reasons.
Have a great trip.