Good choice with Giordanos. It's a gret local favorite. They used to have on in NW Indiana where I'm from, but it went under I think, due to poor planning and lack of funds. It definitely wasn't because the food was bad!
If you think you can handle Chicago pizza again, you should check out CPOG, Chicago Pizza and Oven Grinders. It's located on the ground floor of this brownstone, I think on the northside. CPOG
If you do go, make sure to get the Mediterranean flatbread from the apps menu, because it is nothing short of the best bread in the city, and maybe the world! Comes with herbs in oil, and balsamic, I think.
There's also Grant Achatz's place which is down in the suburbs, if I remember correctly, called Alinea. Alinea
It's very expensive though, and prbably the cutting edge of modern American cuisine in the world. They offer tasting menus, a lot of very small courses; I think Achatz offers 9, 15, and 30 course menus.
For a much more easy-going place (on you and your wallet) is Joe's Bebop Cafe.
. Great southern and cajun style food and barbecue at great prices. And there's always a live jazz band. Also, depending what night you go you may be able to catch the free fireworks show at Navy Pier. I think they are on Wednesdays and Saturdays, but I'm not certain. Should be around 10PM.
There's also a few chain restaurants that started in Chicago that are great. Big Bowl and Maggiano's Little Italy. Bog Bowl has 2 locations, one downtown and one northside, and Maggiano's is in downtown and also scattered in several of the suburbs. Also, the original Pizzeria Uno is located in Chicago, and is a great place to go. A little known fact is that the 2nd Pizzeria Uno restaurant to open is actually called Pizzeria Due, and opened one block from the original to handle overflow from the original Pizzeria Uno. I like to go to Due's, because Uno's seems to be a big tourist attraction. Both places have a lot of history.
Another cool place to go, especially if you want a fabulous dessert, is the Grand Lux Cafe
. They are owned by the same folks who own the Cheesecake Factory (also originating in Chicago, I believe, and located in the basement of the John Hancock building). The food is great, and the desserts are to die for. Be warned though; their dessertsn are made to order and they reccommend you order them at the same time you order your meal, because they can take b/w 15-45 minutes to complete.
Hope that helps!