From http://www.claytonmo.gov :
Shaw Park is located along Brentwood Blvd., just north of Forest Park Parkway, near the heart of Clayton's bustling business district. Shaw Park is the city's oldest and largest park. Mayor Charles A. Shaw first established this 47.47 acre park in 1935. With a welcoming canopy of majestic trees and open grass areas, as well as lovely gardens, Shaw Park offers a respite from the bustle of the city. The parks Century Garden is home to the sculpture 'Molecular Bloom With Single Flower' by James Surls. Shaw Park's most recent additions include over a mile of new walking paths, a new adult fitness area and a large native plant area, The Moneta Garden, with a sulpture by Clayton native Ernest Trova. The Iconic Enterprise Corporate Pavilion serves as an outstanding addition to the park. Shaw Park is home to an outdoor Aquatic Center, which includes a 50-meter competition pool, as well as a diving pool, and a splash and play pool for young children. It also has one of the few remaining outdoor Ice-Skating Rinks in the area. Other amenities include 10 tennis courts, 9 ball fields, 3 playgrounds, and 2 sand volleyball courts. Picnic facilities include the Enterprise Holdings Pavilion (a covered picnic site which can accommodate up to 120 guests), 2 smaller picnic shelters (the North Shelter and the South Shelter) with rest room facilities and 8 paved picnic areas with tables, including 4 large pads with barbeque grills that can be reserved. The Century Garden has cafe tables overlooking the park.
You are looking for a medium sized container near the posted coordinates, not the volleyball courts or the benches. The exact terrain where the Geocache is located may be a bit tricky to walk on, but it is right next to a paved path.