The Chopin is in a transit-friendly part of in St. Louis. It's a seven-block walk from the Westminster to Metrolink's Cortex station. Metrolink serves Lambert Airport, Busch Stadium, and a number of other St. Louis destinations.
If you prefer, it is easy to take the bus to Metrolink. At the corner of Lindell & Vandeventer, catch the westbound the 10 Gravois Lindell, which will take you to the Central West End station. From there it's a 20-minute ride to Lambert Airport. (From Cortex it's a 22-minute ride. to Lambert.) You can take this bus east to the Civic Center Metro Station in Downtown St. Louis, which is across the street from Enterprise Center & Stifel Theater.
Coming from Lambert Airport: If you have heavy luggage and/or don't want to walk from Cortex station, get off Metrolink at the Central West End station (one stop before the Cortex station). From there take #10 bus to the Lindell Park Apartments.
Ask any bus driver to tell you when you are at Lindell & Vandeventer. When you get off the bus, look across the street. Behind the pocket park you will see Lindell Park Apartments, the seven-story building that is home to the Chopin.
Here is a link to Metro St. Louis.
Pro Tip #1: For real-time transit info in St. Louis and more than 100 other cities, download Transit App on your smart phone. Authorize a credit or debit card on your Transit App and you'll be able to buy fares in St. Louis. If you are traveling in on Metrolink from Lambert Airport, you will pay the local fare, not the airport fare.
Pro Tip #2: Another excellent resource is the transit feature on Google Maps.
Pro Tip #3: It's a delightful three-block walk north on Lindell to the city's best served bus line, the 70 Grand.