Personally (and keep in mind, I love driving and visiting new places), I would do this:
Since you want to go to Santa Fe, and from there northeast, this seems like a golden opportunity to travel the famed Route 66. There’s a (really really) really detailed description of how to go West to East on the original route here.
If you just want to approximate it, From Santa Fe, hop down onto I-40 and head east. You’ll go through Amarillo on your way to Oklahoma City. There, grab I-44. You’ll head through Tulsa, Springfield (Missouri), the Ozark Mountains and to St. Louis. Go on through St. Louis and pick up I-55. You’ll pass through Springfield (Illinois) and Bloomington-Normal on your way to the Route’s termination in Chicago.
There’s so much sightseeing and history along that route, just along the parts I’ve visited (from Missouri on). Though money’s an issue, most of it (being of natural or historical interest) is free.
Just on the parts I’ve visited:
[ul][li]Lambert’s Cafe, just outside of Springfield, MO: interesting and quirky restaurant. Costs money, obviously, but you gotta eat someplace.[/li][li]Ozark Mountains in MO: Just plain beautiful. I imagine they’re trumped by the Rockies (never been), but they’re comparable to (though much smaller than) the Appalachians. Really interesting caves and water features.[/li][li]St. Louis, MO: Tons of stuff. You’ve got a really cool campustown, you’ve got an amazing historic riverfront district, and of course, the Jefferson National Expansion Memorial (a.k.a. “The Arch”). If you want to pay a few bucks, you can go up inside the Arch, and that’s pretty cool. It’s the nation’s tallest National Monument at 630 feet. There is a museum underground at its base which I think is free or cheap and of course it’s free to just sightsee in the park at the base of the arch.[/li][li]Springfield, IL: Lincoln’s Tomb, Old State Capitol, lots of Lincoln-related stuff.[/li][li]Bloomington, IL: The home of Steak n Shake.[/li][li]Chicago, IL: Too much to list. Hang out on Navy Pier for free, or just wander around downtown and through Marshall-Field’s.[/li][/ul]
From Chicago, you can hug the Great Lakes and go through Cleveland to Pittsburgh, Philadelphia and on to New Jersey. Alternatively, you could drop down through Indianapolis, cut across to Columbus, then on to Pittsburgh and such.
Anyhow, just some stuff to consider.