A couple of thoughts....

Try this website. They list a number of small hotels. Most don't list pricing, so you will need to email them.

http://www.cartagenainfo.net/

My experience is that the accomodations listed on the major booking sites, are at the high-end of the price range. If you can find what looks to be an reasonably priced room, book it for just one night. Once there, you will be able to find something acceptable at your price range.