The Missouri Botanical Garden is a gorgeous botanical garden established in 1859. Inside, you will find many examples of garden types, like a Bavarian garden, a Japanese garden, a Chinese garden, and more.
Also, you can pay a visit to the Tower Grove House – the house of Henry Shaw, the founder of the yards. It's a three-floors restores house, with periodical furniture and interior Victorian design style.
Additional places to visit in the gardens are the Garden's museum and the Climatron – an indoor tropical climate structure with a beautiful garden inside.
I genuinely recommend visiting the Botanical gardens. You can easily spend half a day here.