Ok it's not romantic unless you are both baseball nuts but Harry Carey's restaurant is like a baseball museum with memorobilia all over. The food is very good featuring steaks and Italian fare. To quote one guidebook the food is much better than one would expect at a celebrity owned restaurant. Of course Harry has passed away but I believe the restaurant is still owned and run by his family.
PS: It's been about 5 years since I was last in Chicago though.
Definitely check out the Hancock building. Great views of the city. People say it's better than the Sears Tower (though I didn't go up on that building).
The hop on, hop off bus tour around the city is also good. Informative and convenient.