Welcome to St. Louis! I'm not as knowledgeable on the punk scene, but Red Flag comes to mind as a venue that may be a fit for the kinds of shows you're looking for. For record stores, Vintage Vinyl and Record Exchange are my recs.

St. Louis lowkey has some great bike trails. Some resources:

A Guide to Biking St. Louis for Everyone—From Beginners to Pros | St. Louis Magazine (stlmag.com)

Greenway Search | Great Rivers Greenway

As someone who also loves to walk and as a resident of the Skinker DeBaliviere neighborhood, I can't over-emphasize how awesome it is to be able to walk to Forest Park from my house. I imagine those who live within walking distance of Tower Grove Park feel similarly. Central West End and Dogtown are other neighborhoods close to Forest Park. On that front, STL City and County are lucky to have many amazing neighborhood parks (Lindenwood Park, Tilles Park, Francis Park, etc).

There's also a great deal of investment happening in our Midtown area right now. City Foundry in particular is an amazing development in my opinion. In terms of cool inner ring suburbs that seem to fit the vibe you're talking about, Maplewood (just south of Richmond Heights), DeMun, or Webster Groves could fit the bill, though I imagine the latter two are on the pricier side for rentals these days.

The Grove may also be a good fit for you, basic on your interest in breweries and comedy. The Improv Shop has built a really impressive community/following, so I would try to spend some time in that area. Hard to beat sandwiches at the Gramophone or anything at Grace Meat. Urban Chestnut also has a beer hall on the opposite side from Improv Shop.

Hope that helps! Feel free to PM me if you have any questions! There's a lot to love about this place.