The best things to be seen in the US are by far all the National parks. I would avoid spending time in too many cities, JMHO. There are some wonderful cities but the diversity of our great parks is where the real treasure of the US is.
The US is HUGE so 4 weeks is not a ton of time to see a bunch if you are driving. If you are flying into Chicago then I would make that your major city to explore and decide what general direction you want to head in (i.e. east, south, or west) and pick some future destinations along the way. I would suggest heading west as you can make a nice 4 week trip out of Chicago and west through the Rockies or Tetons and stopping at some great natural sites along the way. Given that it will be summer, I would avoid the heat of the south. I think Yellowstone, Rocky Mountain National, Grand Canyon, Arches, and Olympic would all be on my list. You could also zig zag around to cities like Denver, Las Vegas, and Seattle on the way to check out other great sites and hit some great pinball spots (Logans in Chitown, PHOF in Vegas, Lyons in CO, and Pinmuseum in Seattle). Could make a real nice trip with those general hot spots to hit along the way.
