You might try Forest Park. It was the site of the worlds fare in like `1903 or something like that. Anyway, when they dismantled the huge Farris Wheel that had been constructed specifically for the worlds fair, the huge center axle was determined to be too big, and either parts of it, or all of it were buried on the grounds. Forrest park is totally safe. One of the old worlds fair buildings is used as a fine art gallery.
You might also try Benton Park. Its an old park surrounded by old Victorian houses. I don't think its in a very bad area. Its close to the Lemp Mansion and Brewery, down in the area of the Budweiser Plant, but west of the plant and north of the Lemp mansion. There's a huge sealed up cave under Benton park, they've been looking for the entrance for years. One of the geology schools came out years ago and conducted experiments to determine exactly where the cave lie under the park, and basically, the park sits on top of the cave......cave is bigger than the park.....hahaha.
Do Not Go to any parks on the North part of town, area by the airport, the area in the west to north of the center of St. Louis. MLK....that area too. Wouldn't recommend it to anyone!
Good Luck!!!