Cheap is a relative term, but under $500, you have quite a few options. Personally, I wouldn't bother with anything other than a Tern or Dahon at that price point. My own experience is that going cheaper than those brands is a quality compromise not worth the price difference.

Check out ThorUSA. Thor is a regular poster here and has a nice selection of Terns and Dahons.

Also, if you are not using it for multimodal transportation or have much need to carry it, you can look at some larger wheel sizes (24-26") if that appeals to you.

Also consider whether you need gearing or not. Going single speed will reduce price, weight, and maintenance.

I have a Dahon Speed D7 which is an inexpensive but great all-around bike.