That is pretty much right downtown St. Louis. I would have no problem walking around there in the day time. You can catch the metrolink and go many places in St. Louis.
I would be sure to go over to Laclede's Landing and have a look around. It's just under the Arch. Neat shops and food. I always like the Spaghetti Factory on the landing. Not so much for the food. It's OK, not fabulous, but I love the funky old building it is in.
Union Station is not far from there. It is a mall type place built in an old railroad station. It's fun to walk around once in awhile.