They haven't updated much this year, but in the past have been pretty active.
http://www.cardsfanschicago.com/

Sedgewicks is definitely the place to watch the Cardinals. As for where to live, you can't go wrong with anywhere on the Northside of the city. It's Cubs territory, but you can't walk one block without stumbling into a bar/restaurant/entertainment.

Sedgwick's is the chief STL Cardinals bar in Chicago.

Lincoln, Armitage, and Sedgwick is the intersection.

The last couple of years the Card have been in the playoffs they've had the game on every tv, and it's all Cardinals fans inside.

They even play "The Heat Is On" during game breaks.

There are other Missouri sports-related bars up here, but Sedgwick's is the one that focuses exclusively on the Cards.

just wanted to confirm joeyart's response...
Sedgwick's - 1935 N Sedgwick St

Been there many times.  Nice atmosphere. Good service.  Decent food.  Always a few Cards fans to talk to.

Block away from a great restaurant:
Zia's

If you get the chance, also go to see Baby Wants Candy.

I grew up in the Evanston -- my parents still live there -- so if you have any questions about that area, let me know (I know my way around Skokie, too!)...good luck with the move.

A little less crowded, a little cheaper rent-wise, but still walkable to games.  Check out your neighborhoods here.

I'm in Roscoe Village - close to public transportation and walkable to Wrigley.  Or if you wanted to hang out with Baseball Prospectus's own Nate Silver, you could move to Wicker Park and party with the scenesters.

I moved up to Chicago around a year and a half ago and live in the South Lakeview area (around a mile South of Wrigley).  Perfect for the younger crowd but a little expensive.  Sedgewicks is a great Cardinal bar, sadly not walking distance for myself so I just adopted a non descript bar with no affiliation with the MLB direct TV package and turned it into my Cardinal bar.  Most Monday through Wed games you can find me, sometimes my Father, sometimes 5-10 other Cardinal fans at Trinity Bar.  It's at Halsted and Diversey.  Great cheap drink specials, decent food, and close to where I live, perfect.  

Welcome to the Windy City!  I've lived here in Chicago for most of the last 12 1/2 years, and have lived all different neighborhoods.  Hope that I can give you some input. And, yes, live in the city.  It is much more fun, and schlepping between the 'burbs and the city for all of your improv gigs will get old very quick.

In college, I lived in East Rogers Park, which is on the Red Line.  Gentrifying, but if you get too far west of the lake (i.e., more then 6-8 blocks or so) it still is a tad dicey.  Great old apartments, though, and the rent is fairly reasonable for a starving (I presume) artist like yourself.  Definitely a synagogue or two in the neighborhood.

The other area you might want to consider is what is sometimes called Buena Park - between Lakeview (of which Wrigleyville is a smaller sub-neighborhood) and Uptown, which is slightly rough, as mentioned above.  Again, on the Red Line and safer closer to the Lake.

I would recommend some neighborhoods along the Brown Line, but I hesitate to steer anyone to the mess that is and will continue to be commuting via Brown Line.  It is in for multi-year construction, and the delays are often horrible.

As for Wrigleyville, lived there once and am reluctant to go back.  The traffic/drunk people/parking situation on game days is horrific, and the area is getting so expensive.  That said, it is fun for a baseball fan to live so close to the action, and you can get a great vintage place if you shell out the cash.  Also, near the Lake and the Red Line.  (My Cardinal-fan husband-to-be, who currently resides in Iowa, wants us to move up there when we get hitched, but I am reluctant to move away from my current neighborhood, where I can walk to my Loop job.  That and I'm afraid that any - potential/future - children may be warped by growing up so close to Wrigley.  Shudder)

Sedgwick's is a decent Cardinals bar, although not for every single game.  (FH and I have been when we were the only Red Bird fans there and consequently not much fun.)  You can walk there from Second City.  

There is also a Cardinals meet up group in Chicago that occasionally gets together and watches or attends games.

http://stlcardinals.meetup.com/18/about/

Good luck with the improv!  I have friends who have/still do it, and it is a tough biz.