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I know nothing about hostels and little about travel options. I’ve traveled a lot in the USA and Canada in the past 13 years but mostly by CAR. I have occasionally used buses and trains. Greyhound is the best bus chain. I've been on a plane six times in my life. United's the best.
Be flexible. I see you plan to use hostels for most of the trip. I've never stayed at one. I’ve probably stayed at a thousand hotels though. Unless I was with a group, I rarely reserved a hotel in advance. If I did reserve one for a night, it was that morning. I never knew where I’d be each night on my unplanned trips. I just winged it. I’ve never had to sleep in a car. I have had to pay some high prices and/or sleep in not-so-nice rooms though. Unless something major was going on in a city that I knew nothing about (producing high rates or no vacancies), winging it often worked for me.
Sometimes you can get a lower rate at the front desk than online. Other times, they’re the same rate. If you know where you plan to be each night, you can check hotel options and rates online in advance. Then call ahead and see what rate you get. If it’s lower on the phone, you might want to take it. Calling ahead also lets you know if something major is going on in a place (festival, wedding, etc). If you travel there and find someplace else to stay, you usually have until 6pm or midnight to cancel the other room without being charged. But check online or via phone first!
If a hotel chain you stay at asks if you want to join its rewards program, say yes! If you get enough points for each night you stay at that chain, you’ll get a free or discounted night eventually (depending on the chain). Hotel rewards programs pay off in the long run.
I’ve stayed at some really nice 3-star hotels for less than $100, sometimes less than $70. My mom uses AAA and senior discounts. We also pick up hotel coupon books at state welcome centers and rest areas. My favorite chains are Marriott (Fairfield, Courtyard, and Residence), Holiday (Express, Suites), and Hampton (Suites). I’ve stayed at Country Inn too. They have free books and DVDs during your stay, plus a full-course hot breakfast. Even Best Western is coming up in the hotel world. One north of Charlottesville, Virginia, is nice and new, like a lodge. Basic hotel amenities for me are a nice bed, good lighting, a hair dryer, a hot shower, cable TV (at least 50 channels), and a decent breakfast (more than continental). The hotel has to be clean!
Back East is much more populated, so you're going to find a lot more accommodation options in most towns and cities, even the smaller ones.
I haven't been to Yosemite. Yellowstone - I stayed in Bozeman, Montana, the night before (back in 2002). The nice 3-star chain hotel was reasonably priced. The drive into Yellowstone wasn't much more than an hour.
I've been to Montgomery only once. I didn't visit Rosa Parks' place but this was a Sunday, with everything closed. I did visit F. Scott Fitzgerald's place that afternoon though. The town also has a Hank Williams Museum.
Chicago - I used to live 3 hours away so I visited often. I loved Lakeshore Drive and the Arts Institute, which is FREE on Tuesdays.
Washington, DC - I used to live half an hour away (and worked there), so I visited often on weekends. The Smithsonian museums, zoo, National Arboretum, and presidential monuments [all free] are the best and most beautiful part of DC. I also like Arlington National Cemetery across the Potomac, which has a Robert E. Lee house/museum.
Philadelphia - you gotta visit the revolutionary era landmarks and buy a philly cheesesteak!
Niagara Falls - the Canada side has the best views and you can get closer to the falls. The USA side requires a lot of walking and you can't park close by.
Have fun! :D