When you say you can't wear slides, do you mean the back of your foot comes out of the open back of the shoe? So, are you looking for something with an ankle strap? Or something that sits higher on your foot, closer to your ankle? (like a gladiator sandal?)
http://www.6pm.com/n/p/p/7300521/c/18.html
Also, can you tolerate a small heel? Do you like wedges? Would you rather a flat sandal? How about a thong sandal (not a beach flip flop, but an actual leather sandal that has a strap between your toes--would you be comfortable wearing that?)
http://www.6pm.com/n/p/p/7193127/c/1430.html
Maybe what would suit you best isn't an actual sandal, but more of a canvas skimmer? Or maybe you whould consider a ballet flat? Angie posted some cute ones that had cut outs so they were airy and summery.
http://www.6pm.com/n/p/p/7307813/c/7915.html
http://www.6pm.com/n/p/p/7350175/c/513.html
Or What about an open fashion sneaker?
http://www.6pm.com/n/p/p/7253319/c/12634.html