Good shoes that fit your feet and gait are essential. They don't necessarily need to be walking shoes or running shoes, but I do feel like they need to be comfortable and supportive. I like the suggestion of going to a running store--but make sure they watch you walk, not run. For me, my most comfortable walking shoes are not the same shoes I wear for running--I have a pair just for walking in the parks (and any other long distances). I also have a pair of Ooofos flip flops that are super comfortable. I wear those on water rides, and maybe for a bit afterward.
The things I've done after running a half marathon and spending the rest of the day in the park include laying on the bed with my feet up on the wall (leg drain) for 5-10 minutes. I feel like an idiot while I do it, but it does make me feel better, so I don't care so much. It really helps with my feet and legs (because once my feet stop hurting I realize my legs are sore, too). If my feet are super sore, I'll run some very cold water in the bathtub or put it in one of the garbage bags and soak my feet for a bit. Some people do ice baths/soaks, but I find the cold water is cold enough. Those two things, coupled with a midday rest and advil/tylenol, seem to do the trick.
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