What you're looking for in a decent but cheap mp3 player. You're not really giving anybody here anything to work with.
Price range. One person's cheap can be overpriced for someone else. Heck, I think $80 is cheap. Of course, that's relative to capacity. Somebody already asked this, but you never bothered to answer.
Capacity. How many songs do you want to put on it? You can probably find something really cheap that's only 256 MB (maybe) or 1GB. It may or may not have memory expansion capability via SD or micro SD cards.
Sound quality. That's pretty subjective. If you're going to use the bundled earbuds that come with most mp3 players, then you're probably not too concerned. But if you're going to replace them with some decent ones, then you're going to want to keep that in mind.
Do you want other features? Video, fm radio, voice recording...
You're asking for a site and somebody already suggested looking at imports from China and you've seemed to have rejected that. Are you looking for name branded stuff? Are you looking for stuff that have been reviewed on sites like CNET? Then you might want to go with name brand players(Sony, Apple, Microsoft, SanDisk, Cowan, Creative, Archos, etc).
Without knowing anything about your requirements, I could suggest buy.com, overstock.com, amazon.com and I'm sure others can chime in on their favorite sites. You could even try WalMart, Target, and Best Buy - either their websites or physical stores.
Good luck.