Yeeeeah, don't wear converses. You're asking for blisters and sore feet in general. Those have no support whatsoever. Grab yourself a pair of running sneakers (with good arch support) if that's what you want to wear into the parks, otherwise, flippy-floppys like poster above me said, not for majority of the day. Went in with flip flops, died about 2 hours in, definitely walked around the parks barefoot for awhile.
You could even grab Crocs (not fashionable, but who even cares) for cheap at an outlet.