With that much money I'd look for good deals on steel downtube shifter bikes. Look for Centurion, Bianchi, Trek, Nishiki, Giant, Fuji, Miyata and any other name brands. I typically stay away from Schwinn, Huffy, Murray, and other cheap bikes. Schwinn makes some nice bikes, but most of them that people post are crap.

Downtube shifters usually indicate a higher quality bike than one found with stem shifters. Also, if you don't know anything about the bike ask people in classic and vintage. They can give you a quick answer. When looking at the bike, check to see if it's in good condition. Don't get a rusty bike. Buying a bike with dry rotted tires, cables, and chain could cost you $100 to repair, and wouldn't be worth it unless you could DIY and get inexpensive parts to repair it.