...generally, yes, polyester is more breathable than nylon. There are multiple different types of weaves (often called different fabrics, actually) made of both types of fibers. What really matters here is that polyester is completely hydrophobic (the fibers themselves don't soak up any water due to their chemical composition, even though water gets into the interstices between them) while nylon is not (though still much better than most cotton weaves).
As far as finding polyester shorts, well, check your local Wal-Mart. In the athletics section (not sure about the women's department, but for sure and certain in the men's), they should have their Starter brand DriStar line. Check the tag (Wallyworld is notorious for horrible product mixing), but the majority of the shorts should be polyester. At least, they are around here. And they should be going on sale soon; it's getting to be fall, and fewer folks purchase shorts in the fall.
If you want to go up a level in cost, Sports Authority or the like will carry polyester athletic shorts as well. If you want a cargo short or such, I'm sure that REI or similar will also carry polyester shorts.
Really, if you want the quickest-drying shorts, look for a thin, loose, open weave on the shorts. The thinner the material, the better, and the more open the weave, the better. I can dry my polyester running shorts after swimming down here in humid FL in about an hour and an half as long as I'm not sitting down. YMMV, though.
(Edited for clarity.)