craigslist has decent deals, but you have to sift through a lot of BS to get there.
for $1200, you're at the very bottom of the price range for a "good" bike. Realistically, you can expect to find older ninja 250's, EX500's, GS500's and maybe a first or second generation CBR (hurricane, or F2).
out of those bikes listed, I'd purchase any of them that's in decent condition for $1200. You'd have better luck bumping up your budget to more like $2,000 though. The difference between a $1200 bike and a $2000 bike is pretty significant.