You should try to buy one for around $50-$75, then take it to a shop for a tune up which will run you around $25+parts. That way you'll spend your $100, and have a trustworthy bike in the end.
For $100, used is definitely the way to go. I'd see if your city has a bike co-op and get it there. If you don't have a co-op I'd start trolling craigslist for a vintage Japanese bike (Nishiki, Miyata, Panasonic). Also I see vintage Raleighs and Motobecanes reasonably priced on craigslist all the time.