I second syd's recommendations for margaritas at Fronterra Grille. I also agree that Keefers is a good restaurant. Nine is hip and lively (and good food) with also a good bar scene and a champagne bar in the center too. I also found the bar at the Sofitel hotel to be pretty cool. I don't think you could ever go wrong with Morton's, Capital Grille, the Palm, or Ruth's Chris...but they have them in so many cities, so if you go to those restaurants at home I'd try something new!

My husband likes Eli's for steak, which is next to the Water Tower, I like Smith & Wollensky because the food is great and the restaurant is on the river, so make a reservation, and request a table by the window.
Greek Isles. or Athena.
We always take our out of town guests to the 96th Floor of the John Hancock building for drinks and the view of the entire city. Hope that helps.

Although I could start an argument over some of the posts, I won't. Rather, I will try to make some recs that are within walking distance of your hotel, rather than sending you off into the neighborhoods.

1) Bar
Rockit which is on Hubbard (one block north from Amalfi). The upstairs can get very loud, but the downstairs is much quieter.

O'Callaghan's is just a good old Irish bar across from Rockit.

The Casbah at the House of Blues Hotel. It's in the Hotel mind you, not in the HOB itself. Live music at night with no cover. Definitely stick your head in here. Avoid the Backporch at HOB.

For something different, directly above the Casbah is 10 Pin. Yes it's a bowling alley, but with a very upscale lounge.

Smith and Wollensky. You can sit outside by the River if the weather is nice. See if the bartender named "Shawn" is working. He is a riot. If Shawn is not upstairs, he may be downstairs at Wollensky's Grill.

Finally, Petterino's on Dearborn and Randolph which is about 3-4 blocks south of the Amalfi. This is another place where the bartender is the real draw. "Ed" is considered one of the best in the City, as is Shawn at S & W. I truly appreciate the work of a genuine professional bartender rather than some 20-something hottie pouring beer (I appreciate them in a different way).

2) Steakhouse
S & W, Ruth's Chris, Sullivan's, Keefer's are all within a stone's throw. Stefani's and Morton's are also close. Morton's just opened a new location on Wacker. Most steakhouses in the City get their meat from one of two main purveyors, so they all really are pretty equal -even the chains. Keefer's is very good but bring money. $9 for soup.
A bit further, but only about 4 blocks is Joe's Seafood, Prime Steak & Stone Crab on Grand and Wabash. They have something for everyone. Took my parents there in December and they still rave about it.
Finally, if you want to experience a meat orgy, try Fogo de Chao at 661 N. LaSalle St., probably a 6 block walk. All you can eat Brazilian churrascaria. I would recommend a late lunch there. The lunch has the same menu as dinner, but it's abut $20 cheaper than dinner. Plus, I find that I need the rest of the day to burn off all that meat before bed.

3) Pizza
Contrary to popular belief there is no such thing as the quintessential Chicago pizza. It can be thick or thin, stuffed or deep dish. Lou Malnati's, Uno or Due, Gino's East are all good and I eat at all of them, but it's really what the tourists eat and then think of as "Chicago pizza". If you want to avoid the tourist crowds I would suggest Bella Bacino's at 75 E. Wacker Drive. It's right next to Hotel 71. About a three block walk from the Amalfi. A little place on the south side of the River that has great thin or stuffed pizza. I wouldn't get anything other than pizza and a salad though. My second choice would be Malnati's. It's about 3 or 4 blocks west of the Amalfi on Wells.

4) Greek
Although you could walk to Greektown, I suggest a cab. I've been to every place on Halsted and the best are Costa's, Santorini, and Greek Islands. Costa's and Santorini are more sedate while at the Islands you can get drunk and boisterous without raising any eyebrows. A fun time. You can eat outside at Athena, but the food is a notch below the others I mention.

Hope this helps, for more research check out metromix.com.
Please report back after your trip. I am interested in your feedback.

Buzzer: Do you know - Is that the original mural at Stefani's - the one from when it was Riccardo's? (Several different panels by several artists.)

As a regular visitor to Chicago, I'll mainly weigh in on cocktails....many of the hotels have very nice, relaxing bars and good people watching. Some of my favorites are the NoMi in the Hyatt off Michigan and the Peninsula Bar.

Rush/Division Area: Sofitel Hotel's Le Bat Bar and the Sutton Place Bar (which is a Whiskey/Randi Gerber bar) These last two lounges are within walking distance of each other.....also in this area are numerous bars and restaurants such as Tavern on Rush, wine bars (Cru?), etc. One of the top steak restaurants is located here as well.

The following list should be fairly close to you but not as far as the Rush/Division area. Although you mentioned steaks, etc. one of our favorite places for drinking and dining is Tizzi Meloul which is mediteranean (may be spelled wrong) or Fontera Grill -- a Chicago institution for unique Mexican food and margaritas. Rockit Bar is a new hot spot listed on your hotel site -- I wouldn't call this quiet but it has two levels of bars and gets quite the crowd. Also near to your hotel for cocktails or food is the new Blue Water Grill (formerly Spago's), Ben Pao's (chinese but good bar), and Brasserie Jo (french). The last group I mentioned are all fairly close to one another and may be walkable if the weather is nice.

Lastly, check Metromix and search what is around your hotel. Good luck and enjoy Chicago!