Unless you're visiting at the coldest part of the year, I would suggest sports sandals instead. Little ones like to play in the fountains, and that way, wet shoes are not an issue (no probs on Kali, either.) A couple of the good, reasonably priced brands for kids are Kamik and Columbia.
Mine doesn't wear sneakers for cold-weather visits, either; he wears Merrell jungle mocs at that time of year; they are very water-resistant and really supportive for serious walking.