M.M.
I'm guessing you'd like to stay in the areas close to the tourist stuff, so stay on Michigan Ave, and take a cab to the United Center (and a cab home, they'll be a ton around after the concert).
The others are right, there's no hotels over there, and nothing else that you'd want to do. So don't center yourself around that.
Take the Amtrak in, and take a cab to your hotel. (I like either The Allerton, which is right next to Water Tower, or The Omni, which is right in the middle of the Mich Ave.)
Make sure to check for street festivals and get out of the tourist areas, though. The real feel of the city is nowhere to be found on the mag mile! :)
Go to Wrigleyville, Lincoln Park, Bucktown, and Lakeview (I'm happy to make bar suggestions, if you're going that route).
Oak Street beach will be walkable from Mich Ave in June, and if the weather is nice, the lakefront is beautiful - especially down by the Museum Campus!
Oh man...now I'm just longing for summer.