Take McDonnel Blvd. (Behind the Large black Renaissance Hotel) until you get to Airport Rd. Turn right, and you'll see a one-way street on your left. This is the street that you are trying to get to. To get there, continue up to the Berkeley High School. The road to the school will loop around in a circle back to that one-way street. The one-way street is at the top of a hill, providing a great view of the whole Lambert field. It is at the top of this hill where you want to be. I'm not sure that you are able to park there, but the spotting is remarkable. It is right next to the tracon tower, and the birds are within spitting distance
Hope you can find this spot, it is THE best. Sorry if my directions are a bit slip-shod, I haven't been to STL for a while. Good luck, and enjoy.