A long weekend may not be enough time so I'll put them in order of what I would do.
1) Comedy club. Best part of NYC. Any of the well known ones are good. Avoid the ones that hand you tickets on the street. Comedy Cellar is the best. Comic Strip Live is really good too and sometimes has free or discounted tickets($20 of drinks required but that is pretty standard). Caroline's is good if you want to see a famous comedian and pay more for the privilege. The shows after 10pm are normally better because it is (edit:) not filled with dumb tourists who get offended that someone said the f word and talked about testicles. The 8pm shows are fun though.
2) Broadway play(which you already have)
3) Statue of Liberty and/or WTC museum. Both are well worth the visit, and somewhat close to each other. The WTC museum takes about 2 hours, so you could go to that in the morning, eat in the area, and then head south to get to the ferry to the Statue of Liberty. We ran out of time to do Ellis Island, but that is included too.
4) Go to Times Square, figure out it sucks, walk through Hershey World, and then get the hell out of there.
5) Go to the Carnegie Deli and get food to go. There will be a long line. That is for people looking for tables. You can walk up the counter and take it to go. Central park is only about a 10 minute walk from there and has a ton of seating. You can buy a drink from a vendor there. These sandwiches are massive. You can split one. My friend and I split a pastrami and neither of us finished it.
6) Since you mentioned smoke, Club Macanudo is pretty good. It's a high end cigar bar. Probably should be dressed moderately nice. Food is really expensive and I believe you can bring your own cigar in for $10 or buy one from them. I was there for lunch and I walked in. Expect a large bill. I think I had $17 nachos but they were good.
7) Walk around the lower section of Central Park. Take a tour on the horse drawn carriage if you feel like having a good experience for a lot of money.

Go to Little Italy for lunch/dinner.
9) Check out the Brooklyn Bridge. On a nice day, it is well worth the visit.
10) Check out a rooftop bar, pay $10 for a drink, get a nice view of the city, and then find some place better to enjoy yourself.
11) Walk into Grand Central station. It is a very nice building.
12) Go to the Intrepid Museum(this would be higher if not for your first visit. It is great, but it really isn't a NYC type of thing)
13) Go an event at Madison Square Garden, which in my opinion is pretty overrated.
14) Walk the high line(This one should be higher as on a nice day it is really good, but ultimately you probably don't have time). It's basically a raised garden walkway that used to transport product from the meatpacking district.
15) Top of the Rock/Empire state observation tower. I preferred the Top of the Rock, but you pretty much know what to expect here. Look at the buildings! Ok, you hungry?
For restaurants, I highly recommend a place called Hell's Kitchen, which just so happens to be in Hell's Kitchen. You'd need reservations until after about 730 when the theater traffic goes away. Porterhouse New York on Columbus Circle is good if you are a steak guy. I'm really not and it is expensive. We really like The Meatball Shop which has multiple locations. There is a place called Pam's Real Thai food which is great and fairly inexpensive. There is a burger place called Burger Joint in the Le Parker Meridian hotel that is pretty cool. Everyone loves Shake Shack, but it sounds like you can get that in Chicago soon. If you want to save some money, take a look at a website called Gilt City. It's like a NYC centric version of groupon that has some good deals.
It's really hard to go wrong with food though. Just keep in mind in your area that there is a massive amount of pre-theater reservations. Don't expect to walk in and get a table near Times Square at 6pm. Make reservations.