Hubski is full of a diverse group of folk who I'd imagine to have taken many road trips. A few friends and myself are looking to take a road trip (from the Chicago area) to anyplace that won't empty our already vacuous band accounts.
Where have you traveled within the US that didn't break the bank?
Do you own a tent? Camping is hella cheap. Drive to Grand Teton. http://en.wikipedia.org/wiki/Grand_Teton_National_Park and take the Beartooth Highway.
I circled the US from the Midwest to Seattle, then down to San Diego and back through the heartland with less than $300. It was a time ago, and there were three of us splitting gas, but you can go a long way eating spaghettios and peas. That's a $2 meal. We slept every other night in the car and at a campground. That way we were able to shower every other day. Campgrounds were around $10-15 for a tent plot, and we split that three ways. The Badlands were a high point. You aren't too far from there. Then you can go on to Devil's Tower and The Crazy Horse memorial.
Camping is the second cheapest way to travel. Crashing with friends is the cheapest. From where you are, Door County, WI, Boundary Waters, MN, and lots of places in western Michigan not named Saugatuck, or around Traverse Bay, though Traverse City is kinda cool. All of these are close enough that the gas cost shouldn't require a second mortgage.
I'll have to figure out where all of my friends are then, haha.
Glacier National Park: I agree with sounds_sound that Grand Teton is amazing but if you've already been to it or want to head north, I highly recommend Glacier. But a couple of months ago I posed the question where have you been that was other-worldly There may be some suggestions there for you. Safe travels!!
If you want to camp and not go that far, there's the BWCA (Boundary Waters Canoe Area) of Norther Minnesota. No motorized boats allowed on MOST of the lakes that make up the area, lots of campers up there in the summer so you aren't ALWAYS alone, but it's remote enough that bears, moose, and bald eagles outnumber people by a vast amount. No cell reception, no motors, no cars, nada. Just some people, canoes, moose, bears, bald eagles, osprey, lots of fish and bugs, and tons of various lakes to canoe across, with lots of portages. Just make sure you no how to read a proper map and shoot bearings, and you'll be fine. Or just bring a GPS device... lol. But this is a trip that takes required gear, and you have to plan quite a bit about where you plan to enter and your route, and you'll need to obtain permits and what not, but they aren't very expensive. All the info you'd need is in the link below. There are plenty of places that rent canoes up near the entry points. http://www.bwca.com/ Since you are coming from Chicago area, figured I'd mention it, because it's not THAT far from ya. But BWCA is REAL camping, ain't no campsite type camping. It's an adventure up there, but it's just gorgeous.
I've been up there a few times, and yes, a couple of the times we had a firearm with us. My buddy that I've gone up there with happens to also be a police officer, so he brought his XD 45 along (he brings it everywhere though). When I've gone without him, we just made sure we had a fog-horn and some bear mace in our gear. Never had to use the mace, used the fog horn once. If you camp right, and pack food properly, and tend and cleanup the campsite for anything that might be "bear attracting", you'll be fine. Alaska is another story, as there bears are much larger. Only thing you have up North here in Minnesota are black bears, which can be aggressive if they have cubs, but they are nothing compared to kodiaks or grizzlies. I tend to see MORE bears at campGROUNDS around Minnesota, than I do straight up camping in the wild. In the wild, they are scared and leave you alone. At campgrounds, they know there are dumpsters and foods to steal, so they just kind of go in there every night. Only seen bears in the BWCA a handful of times, and they were normally hightailing it away from us. We had one group of black bears wander through our campsite one night, but we just used the fog horn and they bolted. I have no idea if this fact is accurate or not, but I've heard that more people get injured and attacked by moose than by bears up around BWCA. Again, no clue if that's complete bullshit or not. But black bears are pretty skittish and runaway. But if we come across a moose, we turn around.