Summer crosscountry trip for non-americans

We are from South America and we have travelled to the US regularly, visiting most of main big cities. What we would like to do now is completely different.
1. We want to visit NYC, SFO and Chicago for a couple of nights each (we have been there before)
2. We want to drive across US
3. We can spend up to 30 days (better if 20)
4. We like small towns, some nature and off beaten track must-do's

While i am studying Lonely Planet USA to find what appeals to us in each of the close by states, it would certainly help me to have your list of cities to visit. Even your suggestions to skip and fly to the next distant place.... Also regarding car options (while we Re generally in lined to premium SUV....it may be good to consider a cheaper option thT still accomodates 3 adults (DH 62, girl friend of ours 52 and me...39 :)...)
Consider we may want to limit our day driving time to 2-4hs. We will want to spend our money on Broadway or nice souveniers rather than hotels...

I have a full year to plan but i would like to have it all ready early enough to "cut the list of cities by half and double my budget" and stil love it.

Thanks folks!

Andy

Welcome!

I would recommend you look at renting a standard sedan in NYC for dropoff in SFO, and drive across the whole country, not using internal flights. It will have ample room for 3 adults and luggage. Our standard sedans are considerably larger than what you are probably used to.