Reddit mentions of Brick By Chance and Fortune

The architecture in STL is pretty special. You can have really interesting time just driving around and looking at buildings, decorative brickwork and fancy cornices everywhere. If you really want to dig in and do homework, you can watch "Brick by Chance and Fortune" on Amazon prime. It isn't thrill a minute viewing, but interesting.

You'll get a kick out of Washington Ave, Lafayette Square, Cherokee, Grand, and Lindell, Soulard, among quite a few others.

I really like the bike trails in the region, might be worth renting or bringing bikes, and riding the Riverfront Trail. (if you really like bikes I can go on at some length)

The Soulard Market is a fun Saturday morning day-drinking/cured-meats/petting chickens occasion.

The City Museum is the thing you'll tell your friends about when you get home. I recommend going Friday or Saturday night, after 5pm. The CM is open till midnight, and the crowds get older/less crowded after dinner. Watching sunset with some beers from the roof is also a nice thing to do.

As far as food goes, you'll find something you like on South Grand, which is the international food street, excellent filipino fusion at Guerilla Street Food, good cheap shawarma at The Vine, char siu bau at Wei Hong Bakery, turkish, moroccan, ethiopian, persian, vegetarian, etc. etc.

The Delmar Loop is another good place for walking, people watching, and food. College kids, tattoo shops, art galleries, restaurants, book stores, etc.

Forest Park is one of the nicest urban parks in the country, with an excellent free art museum, an excellent free zoo, a pretty good free science center, and a pretty good free history museum.

Tower Grove Park is also lovely and worth driving through (unless you can bike it, if you can bike it, do that).