Sounds like an ambitious trip!
You should get online with Craigslist.org and look at the various cities on your itinerary for local info on just about everything. You might be able to find a sublet apartment in NY for your two week stay that won't kill the budget. You might also be able to find locals to hook up with or who will give you great on the spot advice. You can also find drive-away offers on that site.
As for your latest itinerary...
Up to Chicago it sounds great. But train to Milw & to Minneapolis. I currently live in Milwaukee and used to live in Minneapolis. If you really want to see Milwaukee, then the train is a good choice - it's only an hour. But there is no real public transporation here so you'll have to rent a car. There are two Amtrack stops here, one by the airport and one downtown - get off at the airport and take a minibus to the terminal and rent a car there. Easy to get around here, just pick up a map at the rental counter. As far as what to do? Well, there might be a festival or two going on, but by August the season is slowing down on the lakefront fun. You'll be spending most of your time there, or on the East side and downtown. I think 2 days here is enough. The train to Minneapolis might be slow, and the scenery is not that interesting. You could get a cheap quick flight from Milwaukee to Minneapolis on Northwest Airlines.
It's been a while since I've been in Minneapolis, but it's an artsy place so you'll find some highbrow stuff to do.
Fly to Mt. Rushmore? You will miss some of the most beautiful and striking scenery of the upper midwest. The Badlands is not something to miss. Really. Driving up on it from the plains is just astonishing. The scenery after that is beautiful too. Don't fly to Denver. Drive through the mountains - maybe go to Yellowstone and then south to Denver. This is the most beautiful countryside in the world (or close to it). I would nix the train from Denver to KC again because it is flat and boring. Fly. KC to St Louis might be ok via train, or just drive it as it isn't that far.
Little Rock? I'm not sure that's the best use of your time. Here's a cool thing to look into. How about taking a boat trip from St. Louis to Memphis on the Mississippi? And then continuing your boat trip from Memphis to New Orleans? I believe NO is back up to speed these days.
Is there a train from New Orleans to Houston...I'm not sure. But you know you could drive to Houston.
I know seeing the country by train sounds relaxing and romantic, but the Amtrak system here is not that great. Trains are slow and expensive. Sometimes driving is the better option - and you have to rent a car in most cities when you get there anyway. Often the train stations don't have car rental offices nearby so be sure to check that out thoroughly.
There used to be a car rental service here called rent-a-wreck. They have older cars that run well but don't look so good - you might try to google that.
Fly from Dallas to Vegas... Well you've hopped over some of the most exciting scenery in the US. Fun to drive through, great sights to stop at, dramatic sunsets, cool old motels. How about flying from Dallas (you won't need to spend much time in Dallas, just use it as a jumping off point) to Albuquerque, then drive to Phoenix, stop at the Grand Canyon, then drive on to Vegas.
The drive from Vegas to San Diego will drive you crazy. The traffic can be a nighmare. You will certainly get to see the desert, but I wouldn't recommend it in Aug through Oct unless you have a brand new, recently serviced car. I've traveled that route a few times and it is typical to see stranded cars off the road. And despite its being the year 2007 there still isn't much but desert between Vegas and Barstow.
How about flying from Vegas to San Diego and then take a plunge and drive up the coast? Though you will find the scenery nice just north of San Diego, soon it just becomes a big freeway mess through LA county (I used to live in LA too). But with good maps and a stout heart you can get through it. Worth it because just north of the LA mess is great Hwy 1 - from then on it's beautiful.
Three months sounds like a long time, but the train rides will eat up a lot of time. Driving and flying are faster, and not much difference in price.
Also, wondering why you are going so far west only to go east again? You could actually zig zag north and south as you generally go west. Do you have the latest Rand McNally road map? It makes it easier to see the distances. Basically destinations in the east are closer together, shorter travel times, and the further west you get it takes much longer.
I'm not an advocate of polluting the air with car exhaust, but it is a better way to see this country. Try the rent-a-wreck thing, or buying a car, or finding a short term lease. Definitely look at www.craigslist.org for info.
There are lots of hotel/motel chains and they vary greatly in quality and price. We always enjoy finding the little mom and pop places off the beaten track. But there is alway Holiday Inn (getting pricey), maybe Super 8 is an ok chain. Like I said, we look for the old ones not listed in guides or the web.
Anyway, just my thoughts.