Jeff is right - don't wear Cardinals gear to a Cubs game.
A couple of ideas -- since Wrigley Field is almost right next door to the Red Line Addison Street L Stop, you could take the L North to Evanston, which is the first suburb north of Chicago right on Lake Michigan. Orrington Hotel in downtown Evanston is nice. Evanston is about 6 miles north of Wrigley Field. Northwestern Univ. is located in Evanston which has a very pretty downtown area. I used to go to Evanston a lot when I lived in the Rogers Park area of Chicago (far north side) in the 1980's.
Another idea - stay in Rosemont, IL (near O'Hare Airport) take the Blue Line on the L to Addison, then switch to the Addison bus (20 minute bus ride) to take you to Wrigley Field. If you go this route and stay in Rosemont, ask how close is the hotel to the L station in Rosemont. If you will have a rental car, you can park at the Rosemont L station for about $5 and take the L and bus to Wrigley Field.
You can shop around for hotel deals in the Loop/Near North Side of Chicago, but staying in that area will be on the pricey side. If you have a AAA Motor Club membership or AARP membership, check out to see if the hotels have discounts. Summer is the tourist season in Chicago so good idea to start shopping around now for deals. Who wants to visit Chicago on a day like today when it's 15 degrees and snowing to beat the band.
Recommendations -- Shedd Aquarium, Adler Planetarium, Musuem of Science & Industry, Field Museum, Art Institute, American Girl Store if you have will have grandaughters with you who are 10 and under, Lincoln Park Zoo, Millenium Park. I believe you said you would be in Chicago for 3 days, so you won't be able to see everything in 3 days, but you won't run out of things to do.
If you like deep dish Pizza, Chicago is the place to be! Lou Malnati's is my personal favorite.
Taste of Chicago will be held July 11-15 in Grant Park right along Lake Michigan -- it can be very crowded, but it's fun if it is too hot and humid.
Another poster mentioned Chicago Air and Water Show -- that is held from Aug. 18-19 this year -- very crowded but some people love to see the planes, Blue Angel, etc.
Have a fantastic time - May through September is the best time to visit Chicago IMHO.