Another vote for "sport" sandals. We all wear Nike Straprunners at the parks. At first we brought sneakers, too, but we ended up never wearing them b/c we preferred the straprunners.
There are water-compatible sneakers available if you really want a full-coverage shoe with arch support, but don't want to deal with wet shoes; Merrell makes some that are very nice. Sneakers like this have no absorbent materials in their construction, so they dry very quickly. Change your socks and you're good to go.