I use a cute Dav weekender bag that I got from Ideeli or Gilt, can't remember which one. They had a great deal on the Dav brand one day, and I'd been scoping out their rain boots, so I scored the boots, a matching umbrella, and on impulse, threw in to the order an overnight bag. I think the bag ended up being about $25.
The bag makes a great gym bag, since I have it prepared for a pretty wide range of stuff: swimming, yoga, running. Plus shower flip-flops, set of toiletries, etc. It's lightweight but sturdy.
Before this bag, I used a tote that always seemed just a little too small for the job.
Target has some cute, generously sized totes right now, and I sometimes see bags at TJMaxx that would make good, inexpensive gym bags.