On a really basic level as a tourist you're going to want to stay in or near areas called The Loop, River North, or Magnificent Mile (Michigan Ave). Those will generally be the most convenient areas to restaurants, attractions, shopping, and transit.
If you'd like to go to Wrigley (which I would highly recommend even if you're not a baseball fan as it's a beautiful ball park) you might want to try to stay somewhere on or close to the Red Line CTA ("L") train.
I've had pretty good experiences with almost all chain hotels in downtown Chicago. Some of my favorites:
The Wit
The Palmer House Hilton (this is a historical hotel that has a fun old-timey vibe)
The Embassy Suites Chicago Downtown/Lakefront (about equidistant from the Red Line and Navy Pier)
The Courtyard Chicago River North
I would start by checking Expedia and Hotwire to see who's got a good price and then check Google Maps and Tripadvisor to see who's in a good location with reasonably good reviews.
There are some great Groupons for summer fun in Chicago right now. Here's one for Seadog Cruises that might be a hit with the kids:
http://www.groupon.com/deals/entertainment-cruises-chicago-4
Aside from Wrigley and Navy Pier, I'd recommend spending an hour or two in Millenium Park. The Cloudgate sculpture and nearby fountain fascinate kids and make for some great photos. Also, Lincoln Park Zoo is free and very large and Lincoln Park itself is pretty nice. Finally, you might enjoy the Field Museum of Natural History (especially if the boys are into dinosaurs) or the Shedd Aquarium for an outing.
Hope you have a great trip!