Hi, I will send you an email, but adding some info here as well.
Welcome to Madison! As Robert mentioned, HMGS-Midwest is an active organization out of the Chicago area that holds events in Wisconsin as well.
I'm over in DeForest (other side of Madison from you) and there are a ton of local options for you.
Stores-
There are a number of great game/miniatures stores in the area (mostly games, but with some miniatures).
Noble Knight- Southwest side- enormous selection of everything you can think of and a ton of gaming space
Pegasus Games- A classic game store on the west side, and oldest game store in the area
I'm Board- Great game store in Middleton and Sun Prairie with lots of play space
Misty Mountain- East side store with tons of gaming space and wide assortment of stuff
There are a few smaller stores as well, but they are more card focused.
Local Cons-
There's a lot of great events in the area each year with the notables being:
Little Wars (April, Chicago)- Miniatures focused and run by HMGS Midwest
RockCon (October/November, Rockford)- Miniatures focused show about an hour from Madison.
TundraCon (January, Appleton)- Miniatures focused small but great show.
GameHoleCon (October/November, Madison)- A mini-GenCon in Madison
Nexus (June, Milwaukee)- More of an everything show with costumes, games and more
There are a number of other shows in the area, but those are the more notable ones.
I will reach out to you on gaming directly.