I think that looking for a state first may be the wrong approach. You should probably try and get SOME idea of what it is you want to do, or at least what field you'd like to work in. Some jobs you can get anywhere, of course, but even so, if there are any jobs you're thinking about that ARE region-specific, then moving to that region will expand your options.
That said, if you do want to search by state, this would be a good place to start...
http://en.wikipedia.org/wiki/List_of_U.S._states_by_unemployment_rateGeneral comments:
Oklahoma is indeed a quite nice state, if a bit over quiet and also extremely conservative. Austin, Texas is a bit more lively, but I'm less sure of the job market around there - some of Austin's titans are faltering like Dell.
The nearby Dakotas have very low unemployment, and are actively recruiting Minnesotans to come over and live there as we speak. However, the economy there is largely based on, uh, resource management I suppose - hard labor outside, basically, for things like mining, and managing / fixing machines as well.
The San Francisco real estate market is, last I checked circa 2005, the most expensive market in the country (New York being #2). They've some really dumb rent control laws that had the opposite effect, basically.
The DC region is indeed incredibly expensive, as noted earlier; find roommates (there's a massive housing shortage there and the road system is congested). But the job market is pretty stable there; there's a lot of government, defense contractors, etc. who are pretty safe from budget cuts (AgentKing?). If you have any desire to work in government (good benefits at least!), it's worth a look. The one thing I will add is that many government jobs have strict hiring requirements and can hire based off a "score," and an Associate's Degree may not cut it for some of the better starting positions. However, the government posts all job openings online nowadays, so you should be able to give it a look easily enough and see if there's stuff you're interested in.
Speaking of government, I should add that the FAA is actually hiring, something I'd know more about than your average gov't. agency due to my parents working there. Their headquarters is in Oklahoma City (go figure), and also have a big huge center near Atlantic City, New Jersey (my home region). Southern New Jersey is pretty cheap to live in, for what it's worth, but the only good jobs are with the FAA or the casinos. Oklahoma already covered, they're cheap too. If you have any interest in being an air traffic controller, those jobs are everywhere, including not at airports (en-route centers for while the planes are in-between airports, natch); they used to take people without bachelor's degrees, as well. Not sure what the rules are now; mentioning it mostly because there was a big hiring surge in the early 1980s after the strike, and I wouldn't be surprised if there are plenty of openings for those retiring after ~25 years service, and because ATCs are traditionally mocked as playing video games for a living.
The Philadelphia area is of moderate expense ($500-750 rent?). The economy there is also kind of getting by, though I'd be hard-pressed to name a specialty; it was lawyers back in the day, but not anymore, I think. It's certainly the only part of Pennsylvania who's economy isn't completely in ruins. Western PA... uh, Pittsburgh is really cheap to live in, but for a good reason, everyone left. There are jobs in medicine (some very good hospitals in the area) and academia (universties) and that's about it. Same with nearby Buffalo, NY; medicine or nothing for jobs, but at least housing is dirt cheap. The rest of upstate New York is horrible; more cheap housing but not even hospitals for medical jobs. (Okay, Albany has some jobs.)
The New York / NJ region is where I live currently. Finance, media, and entertainment are the biggest things of note about NYC at the moment, and all are in a bit of trouble at the moment. So the job market isn't as good as DC's, I'd say. On the bright side, public transportation is much better here than in DC; I get by without a car just fine (which saves a LOT of money to offset the high rents), while that's problematic in the DC Metro region unless you live in DC proper itself. I currently pay $930/month rent in Manhattan, for what it's worth, and actually we're having a bunch of vacancies open up right now with people graduating and all. There are a decent amount of openings for cooks and bartenders if you're looking to get a job immediately while you look for something else.
And though I wouldn't normally recommend this, AAA has a good point, assuming you're fine with the fairly unique constraints that living in Afghanistan/ Iraq brings. Cost of living: 0, they pay you to be there. You can grab a Bachelor's later on Uncle Sam's dime, and if you can manage your way into something not the infantry, that can certainly be parlayed into useful skills later. (Medic, mechanic, pilot, translator.. all good stuff.) Obviously not an option if you're not okay with the risks involved, but economically an extremely solid choice.