Good Food near United Center
There aren't a whole lot of good places in the immediate vicinity (and I'm not sure whether there are even *any*, although that depends on how specific you are being with the words "good" and "near"). Most people I know with season tickets to the Bulls eat elsewhere and then go to the game. Obviously there are plenty of restaurants all over the greater downtown area, which is only a few miles from the stadium. Restaurants in Greek Town, River West, and the Randolph Street area of the West Loop are marginally closer, but are still a mile away or more. one sixtyblue is a nice restaurant at the far west end of that Randolph corridor, so it's slightly under a mile. (Their website says, "leave your car with us if you're headed to the game. Ask your server for details.") But if you're expecting a nice place within a block or two of the stadium, you're probably not going to find it.
160 North Loomis, Chicago, IL 60607
Last year before a Hawks game I went to WestEnd @ 1326 w. madison about 6 blocks E. of the UC. Sports bar with really good burgers and beer. Even better they have a free shuttle to the UC. They do it for Bulls too but with no season so far that's not a concern. Practically next door to WestEnd is Viaggio Italian restaurant. Haven't been but they got good reviews on Check Please! With regard to WestEnd, I got there about 5:30 for a 7:30 game start and got the last seat at the bar so go early. There are other places....BillyGoat, etc and some of those may have shuttles as well. I know that the shuttle is what sold me on WestEnd to begin with and then the food was good too. If you have a vehicle, Little Italy isn't far away as are the restaurants over on Randolph...Girl and the Goat etc.
I live near the UC. Next to 160 Blue, on Odgen and Lake is La Luce, decent Italian. On Monroe there is Carmichael's Steakhouse. They offer a shuttle as well. Macello on Lake Street. Beer Bistro on Madison near the WestEnd already mentioned. Union Park on Racine.
1393 W Lake St, Chicago, IL 60607
1061 W Madison St Ste 1, Chicago, IL 60607