Unfortunately, summer in Chicago is not a very good time to see theater. The folks recommending storefronts are on the right track, but most of the really swell storefronts go dark in the summer months. If you want a taste of the Chicago storefront experience, check out Theater on the Lake. Every summer they gather some of the best storefront/non-equity theater that has run in the previous year and give these productions one week runs. Since the seasons not over, the productions that will be appearing have not been announced yet. You can check out their website for updates:
http://www.chicagoparkdistrict.com/events/theater-on-the-lake/ The big houses run shows in the summer in an attempt to snag the tourist crowd. There are some things that really look worthwhile on the schedule this summer.
Steppenwolf has a Bruce Norris world-premiere directed by recent Tony winner Pam Mackinnon. The cast has been announced yet, but I'd imagine it'll be worthwhile.
The Goodman has a major revival of Brigadoon with up and coming Chicago musical director Rachel Rockwell. Word on the street is that this production may lead to greater things. The Goodman is THE prestige theater here in Chicago, so it's worth the trip just to see the institution.
Chicago Shakes is doing Henry 5... but there shows are always hit and miss. The throw a ton of money at them, but I'm not sure they're always worth it. The theater itself, set out on Navy Pier, is absolutely beautiful. The view of the city skyline from the top floor bathrooms is the best view in the city. I'd check the reviews before I'd buy a ticket, though... and the tickets are EXPENSIVE. If you're there later in the summer, you might check out their Children's Show. They do one every summer, and they're usually fantastic. In the past they've done shortened Shrek, shortened Beauty and the Beast, shortened Suessical... etc. Though it sounds uninteresting, these productions are always fully produced and often star the cream of the Chicago theater community. They haven't announced what they're doing yet, but keep an eye out. Tickets are usually about 30 dollars.
Victory Gardens is doing Death and the Maiden with Golden Globe winner and Grey's Anatomy star (former star?) Sandra Oh. It's directed by the artistic director Chay Yew and everything he's done recently has been super-duper-fantastic. It's a significant theater that often goes unmentioned when people ask these questions. It's currently housed in the Biograph theater, which is where gangster John Dillinger saw a movement before he was shot in an alley around the corner. If you're lucky you'll see a Chicago Gangster Tour Bus when you're leaving the theater.
Of course, The Last Ship, will be trying out in Chicago over the summer... if that's of interest... but it's not quite what you're looking for.
Second City is almost always a good choice. The main stage and the ETC stage should both be great choices. Too Much Light Makes the Baby Goes Blind is a Chicago long run... but it's more slam poetry than it is Improv. Slam Poetry makes my skin crawl, so... you know... if it's the kind of thing that you like it'll be the kind of thing that you like. Also, take a look at IO. They're the beginning and the end for long form improv. Literally nobody does it better. See TJ and Dave for the best improv in the country (they do the Sonic commercials, if you're not familiar with Improv). See the Deltones if you'd like to try an improvised musical. See the Improvised Shakespeare Co if you wanna see... well... I'm sure that's clear. If you can't see any of those... see a Harold show.
That's all I've got for now!
Jesus saves. I spend.
