My favorite pizza place is Giordano'sGiordano's Pizza. There are a couple of locations downtown. They have amazing deep dish, which is a Chicago tradition.

Some other suggestions:

Have a drink inside the The Palmer HousePalmer House Hotel. Absolutely beautiful inside and very close to Milleneum Park.

Go up on the Willis TowerSear's Sky Deck. Even if the line is long, they move you through quite efficiently and once you are up on top, you can stay as long as you want.

Take a Chicago Architecture TourChicago architectural boat tour. I live in Chicago and this is the one tour I can do over and over again.

I would also suggest taking in a Chicago neighborhood and leaving downtown at least for a couple of hours. You can take a cab or ride the Red or Brown line trains.

Check out some of these fun neighborhoods

Wicker Park as Tandy suggested

Andersonville

Wrigley FieldWrigleyville

Uptown

Lincoln Square

Lincoln Park

Enjoy yourself in my hometown!

Oh, since you're going to be going to  Millennium Park early on, there are a few brunch spots that I really love around that area!

• Wildberry Pancakes & Cafe: Your standard breakfast fare with a little more pizzazz.  Their pancakes and french toast are amazing and depending on how you order them, can be drenched in chocolate sauce, berrries, etc.  By they way, they have RED VELVET french toast.
  
• Lavazza Espression: Come here for the coffee and sandwiches.  This fancy little place has such amazing coffee creations!
  
• Pittsfield Cafe: Doesn't seem as popular as the other two.  More of a hole-in-the-wall and a hidden gem.  Also your standard breakfast fare, but more traditional and down home.
  

As for night life, check out the  Wicker Park neighborhood.  My friends and I checked out a few bars and music venues there and it was decent.  The one bar that stood out the most was  Violet Hour.  Really creative cocktails if you're into that.  I would suggest just Violet Hour even if there weren't anything else to check out around it!

Have fun in Chi-town.  It's a pretty fun city!

I have a few food recommendations:

• Gene's Sausage Shop: The sausage here is one of my favorite foods in Chicago.
  
• Au Cheval: A fun bar with great burgers. Au Cheval means you can get anything on the menu with a fried egg.
  
• Uncle John's BBQ: Do yourself a favor and order the rib tips.
• Lula Café: My wife and I stop here whenever we're in Chicago. It's a fun neighborhood place. I like the vibe.
  
• Margie's Candies: I am a big fan of coffee ice cream. A scoop of that with Margie's hot fudge is great.
• XOCO: The hot chocolate is killer.

For a must-do thing, if there's a game, you should check out Wrigley Field. Wrigley has been the home to the Chicago Cubs since 1916. This place is built on tradition. When I'm here I always go traditional with a Ball Park Frank, Chicago style.

I second the Willis Tower recommendation. Be brave and stand out in one of the glass boxes. If you like theatre check out what Steppenwolf Theatre Co have on the go or if comedy is your thing you need to see Second City. One of my favourite places was the The Art Institute of Chicago and I had a lot of fun taking a Segway tour of the park with City Segway Tours. River North is generally a good neighbourhood to catch some live music or hit a club. I meant to go to Howl at the Moon but crashed instead. Hope you have a great trip.

If you like architecture,  Chicago Architecture Tour is awesome. Great tour.

Gibsons Bar & Steakhouse is an old school Chicago-touristy steakhouse. Worth it to pop in for a drink and the food is good, but i prefer some other spots to eat. It is in a lively area on Rush with lots of bars & restaurants around.

Hugo's Frog Bar & Fish House is next door to Gibson's and has the same food as Gibson's steak house, but easier to get a table and maybe less expensive. Different vibe than Gibson's, but also a good choice. 

At  Paris Club is another good spot for drinks.

Kingston Mines is an old school Chicago blues bars. Live music every night. Some great music and even better people watching. Lots of other bars in the area too. Well worth a stop for some old school Chicago vibe.

The roof at  Epic is a great option if the weather is good. It's a nice American restaurant.

Japonais Restaurant is a good spot for sushi. Feels more like ny than chicago. Cool setting on the river, but wouldn't be my first choice unless you are dying for sushi.

And this is totally random, but I used to walk and drive by Garrett Popcorn Shops all the time and it didn't matter if it was summer or the dead of winter, there was always a huge line outside. For popcorn. Couldn't figure it out. Then one day my wife and I waited in line for a half hour to get some. It's delicious. Not sure its worth the wait, but if you're strolling around Michigan Ave and shopping and feel like a snack. Not a bad option.

By the way, keep this one in your back pocket: The Wiener's Circle. A legendary late night, drunken eating place. Dogs and cheese fries. Only appropriate late night after the bars. If you're drunk and in the area, go here and be prepared for a bizarre experience.

Do you have a place to stay yet? If not,  Sofitel Chicago Water Tower is in a good location. Walking distance to lots of restaurants. Good bar, etc. Easy cab ride to most of my recs. The Peninsula Chicago is probably the nicest hotel I've stayed in. The afternoon tea is excellent. I just love finger sandwiches. There's also  The Talbott Hotel. Haven't stayed there, but friends really like it.

Check out Yokes at 1120 S Michigan Ave for breakfast.  Great place.  As far as pizza goes, it's a debate that will never end among Chicagoans. Lou Malnati's Pizzeria is my number one.   Giordano's a near second.  Aside from pizza for dinner, look into Joe's Seafood, Prime Steak & Stone Crab at Grand and Rush.  It's one of the best in Chicago and has everything to offer at a fair price.   It's based off of the Joe's Stone Crab in Miami Beach...highest grossing restaurant in the country for a number of years.  The Chicago location is owned by Lettuce Entertain You, a massive restaurant company in Chicago. Most of their operations are great choices for any style of dining- I'll admit I am slightly biased towards them as I used to be an intern there.  Have a great trip.

You should take the  Chicago Architecture Foundation River Cruise.  It was one of my favorite things I did during my year living in Chicago.

As far as food goes, there are lots of great steakhouses, but Gibsons Bar & Steakhouse was always my favorite.

Since Museums and Parks factor into your travel plans so far, I wanted to add a few tips for the venues you mentioned (and suggest a couple more venues you might like).  Millennium Park is a must see attraction on foot, so bring your camera with you; when it originally opened there was a "ban" on photographs, but you can feel free to make your own snaps before venturing to the photo museum.  A short walk from there is The Art Institute of Chicago which features more photography, and also give you a chance to relive your favorite scenes from Ferris Bueller. Afterwards you might consider taking a Chicago Architecture Foundation River Cruise to tour the local landmarks more quickly.

And a couple rainy-day suggestions for Chi-town: Adler Planetarium is a great place to relive your childhood dreams as an astronaut looking at the stars.  But another hidden gem in Chicago is a bit beyond walking distance Museum of Science and Industry; you can lose a whole day walking through this highly interactive museum! 

Hey Sunil, I would recommend S & G Restaurant for breakfast. The owners are awesome and it's been a favorite breakfast spot of mine for a few years. Two other dinner spots I like a lot are Quartino and Tango Sur.