In Chicago for two nights - what can't we miss?

In My Humble Opinion
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We’re going to be in Chicago for May 13th and 14th; so far we have only a ballgame at Wrigley Field planned. What else are the can’t miss sights of Chicago that we can fit in to two days? Any other tips on what not to do in Chicago would also be welcome (like what time do we not even try to drive around).

Oh, suggestions on where to stay while we’re there would also be welcome. We’re thrifty folk - clean budget hotels are our preference.

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I didn’t know if you’d seen this: Chicagoans - Another thread looking for recs! Yay! - In My Humble Opinion - Straight Dope Message Board

Isn’t it weird how topics you’re thinking about come up right when you need them?

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I did not see that thread. Thanks, Dung Beetle. If a mod wanted to close this thread, that would be fine by me - I’m just going to mosey on over to the other thread.