I did your trip last summer at the exact same time. 44 states in 7 weeks, 13000 miles, staying with friends and family in San Francisco, Seattle, Denver, Chicago, Indiana, Baltimore and Charleston. It was great fun and I want to do it again soon. Here's some advice.

Being a life-long desert dweller (Phoenix, Arizona) I suggest avoiding my town at all costs in the summer. Also, stay away from Texas entirely. Don't even drive thru--it takes forever. The heat and humidity in the south is brutal so I'd avoid Georgia, Alabama and Mississippi too except, of course, to drive thru with the air conditioner on. The French Quarter of New Orleans is fabulous, especially for music lovers. If you like the outdoors, nothing beats Northern California. If you like Americana Kitsch, go to the Black Hills of South Dakota and bring your camcorder to film the buffalo herd. New York City is a great place to visit for many reasons. Stay away from Las Vegas unless you have a lot of money to burn. Charleston, South Carolina is a neat town and the beaches there are much less crowded than in Florida.

Don't drive a car in Boston, New York, Chicago, Los Angeles or San Francisco ever, or in any other major city during week day rush hour. The driving "problem" is not so much getting from city to city as it is getting to someplace inside the city. You should have no difficulty at all, for example, driving from Denver to Chicago. It's once you get to Chicago that the problems arise. I would avoid large cities entirely unless you plan to stay a couple of days and you can meet someone there who will drive you around.

Plan your trip around places you can stay with friends. There are many, many sights to see in America but the joy is greater seeing a lesser one with a friend than a great one alone.