So far, I've been able to visit three game stores in the area:
Battle Brothers. This store focuses on miniature war games - primarily Warhammer. I really like the store and the staff. What I look for in any FLGS is what they offer beyond selling product and Battle Brothers offers anything new or experienced players would want in support of a Warhammer hobby. Want to learn to paint miniatures? Besides selling paints, brushes, miniatures, etc. They have tables and areas for painting and events for teaching you how to paint. They have events teaching you how to play and the staff will set up bespoke sessions to help you get started and will help match you with other players. The staff are knowledgeable about the product, enthusiastic about the hobby, and helpful without being pushy. It is not a particularly large shop but there is a surprising amount of play space and it had a good number of groups playing at the various tables on the weekday evening I visited. I walked away with the Warhammer 40k Core Book. I really don't have the time, storage space, and money to go all into Warhammer, but I'm thinking of buying, painting up, and playing a Combat Patrol set.
Beyond the Board. Great FLGS for board games. Their business model is focused on renting out tables and serving food. They have a large, well-curated library of board games you can choose from to play. Great for trying out a game before buying it or just enjoying playing different board games even with no intention of buying them. You can schedule time with the staff to have them teach you and your group how to play a game. They also have open game nights twice a week. The food is quite good. It is a great place to go out to dinner with friends and combine that with a game night. No TTRPGs however. I'm sure I'll be going to the occasional open game night. TTRPGs are what I'm really hankering for, however, so I'm not sure I'll be a regular.
Boardgame Barrister (Bayshore). I visited one of the three Boardgame Barrister shops in the Milwaukee area. Its in a large shopping plaza and is really just a store. There really isn't any play space. They have one gaming table, mainly used for scheduled events. It reminds me of a Kaybee Toy Store but just for board games. They don't carry any TTRPGs. I didn't stay long and spend more time looking at the TTRPG shelves in the Borders Books a couple shops down. One their website, however, they do have the occasional D&D game that you can sign up for, but it just seems like it would be a weird venue to try to enjoy playing a TTRPG. I don't expect I'll be going back here.
@JLowder posted above that different Boardgame Barrister stores have different play areas, so I might check out the other two stores to see if they are more TTRPG friendly.
Coming from Minneapolis, I have to admit to being underwhelmed with the TTRPG scene in Milwaukee. If I were to set up a public game myself, I'd probably reserve a table at Beyond the Board. It is a great venue for playing TTRPGs, even though they don't sell any TTRPG material.
I'm planning to make a pilgrimage to Noble Knight Games in Madison. I've bought a few out-of-print and hard-to-find games from them online in the past and it'll be nice to see a huge store with a large gaming hall. I don't see much TTRPG stuff on their event calendar. They do have Adventures League, but they are all on weekday evening. There is no way I would be able to get off work and drive the hour and half to make the 6pm start times.
On my list to visit this weekend are Warpstone Games & Lounge and TK Games. I'm cautiously optimistic about Warpstone Games. They have a TTRPG area open on Sundays--but not Saturdays :-(. I don't see any scheduled TTRPGs on their event calendar, but they do organize a living world D&D (Living Leagues). I can't commit myself to an ongoing campaign though. I check it out on Sunday, see if they have a community bulletin board. Maybe I'll post for players for a few one-shots of let common systems.
I'll check out TK Games, but I'm not optimistic. Their event calendar is empty and the Store News page hasn't been updated since 2016.
Lastly, I did find a new place,
Oddwillows Game Haven. It is the only FLGS in a somewhat reasonable driving distance that has TTRPG one-shots on its events calendar (and they are not all D&D!). Its a 30-40 minute drive, but for a 4-8 hour game, I'm willing to make the drive.