In your $100-200 price range, I'll give you one to look for and one to avoid:

Look for: Fuji (Marlboro) folding mountain bike. This was a promotional bike that you had to pay cash + 8000 Marlboro points - each ciggy pack was 5 pts., so what, half a lung? Anyhoo, the drivetrain and wheels are cheap, but the folding mechanism is ingenious (seatpost secures entire bike, which can't be ridden without it), and it's fairly easily to upgrade the drivetrain and wheels - there are posts here when people have done exactly that. My fave cheap folder, often goes for $50-100.

Avoid: Schwinn Loop. Had one earlier this year, and it's an abomination. I'm a mechanic, and for the life of me, the V-brakes were so cheap so as to defy adjustment. Hinges were cheap, frame was cheap and wobbly. A good example of what not to get.