Step 1: From the airport, get onto a Metrolink Train heading eastbound.
Step 2: Getting around the Central West End.
Exit the Metrolink platform and go up the stairs on the western end of the platform. This will put you in the center of Washington University School of Medicine / Barnes-Jewish Hospital campus. Here is a Google Map that highlights Workshop locations, hotels and recommended restaurants in the area.
Step 3: Feeling adventurous?
St Louis has Uber, which makes it easy to get around and explore the city in relative safety. Here are some neighborhoods and attractions that you may be interested in:
Step 4: Going Home
Simply reverse your steps in Step 1, with one important detail: Get on a Westbound Red Line train. Way-finding on Metrolink platforms is not very good, compared to most other mass-transit systems. Be sure to be watchful for a train with red signage displaying "Lambert Airport" as its final destination.