Depends on your age and the rest of your wardrobe.. If you're in your early-mid 20s or younger (as much as I hate them) you really can't go wrong with a pair of converse in white or cream colours
I'm sure you know what they look like:
http://images2.chictopia.com/photos/ChristophSchaller/9248179142/red-cos-shorts-black-h-m-cardigan-gray-h-m-shirt-white-converse-shoes_400.jpg
Also notice the kneefold; if you remember my last posts here about the importance of the knee fold on shorts

Now if you're in your mid-late 20s and don't go to college/school but still need casual shoes for work (or spare time) I recommend fuzzy leather shoes (sorry I forgot what they're called, here's a picture)
http://i01.i.aliimg.com/wsphoto/v1/1394697913_1/Designer-shoes-Miskeen-font-b-men-b-font-casual-font-b-boots-b-font-genuine-cow.jpg
http://www.bexley.com/Bexley/image/Talloires-velours_gris.jpeg
OR leather sneakers give a great casual look... but you said you don't want sneakers :/
They're called chukkas brah. And wearing chukkas with shorts would look weird as heck I think.