Chicago!!! Wrigley is awesome, so I'm glad you're going. I would break it down by neighborhood.
West Loop: trendiest part of town, high end culinary restaurants and newer, trendier spots. Definitely good people watching and will feel like the most vibrant part of town. Think of it as Chicago's answer to Soho in New York. Girl and the Goat is the most well known restaurant in this neighborhood (but there a loads of good options). Momotaro is my favorite sushi in the city and is in West Loop. At a minimum, spend and afternoon / early evening walking around, popping into bars. Try to get a burger at Au Cheval.
River North: I think you can skip it. Used to be what West Loop is now, unfortunately now it doesn't have the same energy that it used to. Worth walking around if you want to see the big building on the Loop. I would recommend doing with River Walk and exploring River North by foot.
Gold Coast: (where I live) I think it's the prettiest neighborhood. Plan a walk down Astor St, between Division and North Ave, prettiest brownstones in the city. On the south end of Gold Coast is Viagra Triangle. This is a must visit for a drink and or dinner. Gibsons, Hugo's, Lux Bar, Maple and Ash. A martini at Gibsons is a rite of passage. Small park in the middle of the 'triangle' that you can smoke in. Biggs in just one block west. I would also say get a Guiness at Butch McGuires (a great bar, with good food and a fun late night spot if you're looking for it).
Lincoln Park: more of a family neighborhood, but spending some time walking up and down Armitage is worth it. Some great restaurants here too. Boka is super high end and worth it. Summer House Santa Monica is a favorite with women. I would point you towards Riccardo Trattoria for a local only, excellent Italian meal. Gemini Bistro is a great, casual restaurant that's been a staple of Lincoln Park for ages.
I agree that you need to get an Italian Beef - I like Mr Beef on Orleans and Superior. You should also think about hitting up an old school Italian grocery for amazing subs. Bari in West Town (not West Loop) of JP Graziano in West Loop (probably easier if you're spending time there).
Other great Chicago Staples:
- Gene and Georgetti (very close to Bavettes)
- Gilt Bar (next to Bavettes and same owner)
- Twin Anchors (ribs in Lincoln Park)
- La Scarola (old school Italian for dinner)
- Monteverde (West Loop, elevated Italian)
- Galit (Israeli in Lincoln Park, phenomenal)
- Asador Bastian (Spanish steak house in River North, unreal and expensive)
- HopLeaf in uptown (north of Wrigley)
- Lots of options in China Town (on the south side).