I'm going to respectfully disagree, at least partly, with the "stay off the interstate highways" crowd. Some Interstates are beautiful and lovely and scenic. Some are uninteresting and, well, banal even. But the exact same thing is true about secondary roads; some are wonderful, and some are a steady diet of "scenic" strip malls and big box stores and used car dealers. It's best to figure things out on a case-by-case basis.
Anyhow, here a few general suggestions of places and things to consider seeing. Naturally a lot depends on what you're interested in. Needless to say, there's far more omitted than listed.
- Yellowstone...yes, it's western, and popular, but it's a beautiful and geologically unique (and fascinating!) area.
- I liked the Badlands quite a bit.
- If you like cities and museums, Chicago has a lot to offer. (Unfortunately, so far as I am aware at least, convenient camping is not particularly among them.) Definitely make use of public transit in Chicago rather than attempting to drive and park in the city.
- In New York state, Letchworth State Park and Watkins Glen State Park (among others) are spectacular. Niagara Falls is certainly worth seeing much, though I'm not personally taken with it like some people are.
- Washington, DC has a tremendous amount to see and do, even if you aren't particularly interested in US history or government. Many of the (very numerous) museums are free, including all the Smithsonian Institution ones. A good, and very reasonably priced, option for camping (no hookups) is Greenbelt National Park in Greenbelt, Maryland. From site 145 on the D loop there, it's about a half hour walk (about 2 km, I think) to the College Park Metro station.
- It's not coastal, but Skyline Drive (Shenandoah National Park) and the Blue Ridge Parkway (from there to the Great Smokey Mountains National Park) are fantastic.
- Fort DeSoto park, in St. Petersburg Florida, is very nice.
- New Orleans is a fascinating city. I think I camped at St. Bernard state park quite a few years ago when I camped and toured there.
