I go there to fish, but there is a short trail that can be fun. The last few years, I've been going to Montauk for a week around Labor Day. It makes for a very relaxing week. I fish a little, read a little, nap a little. This year, I made a point of just walking around the park. I hiked the official trail, but I also just walked around, usually in the afternoon, when the fishing was slow.
It's quite a drive, almost 3 hours from St. Louis, so I don't go there anymore unless I can stay at least a couple of days:
More information can be found at the park's web site.
There's a lot of wildlife in the park. More than once, I've seen deer feeding in the shallow water:
And, less happily, quite few skunks and racoons. Labor Day seems to coincide with some important date on the skunk social calendar--their sqawling and smell fills the campground at night.
I wouldn't go to Montauk just to hike, since the trails aren't long enough to justify the drive. But the trails do offer diversion to the fisherman: