Is the super bowl any different than any other NFL games? If not, then you ABSOLUTELY CAN NOT show it in a movie theater even if it is for free. IF you are a movie theater that regularly serves alcohol and food, then yes, you can. But if you are a regular movie theater that only sells regular concessions, then you're out of luck.
I know this personally, as I received a cease or desist letter from the NFL for showing MNF games for free, even though we served food (but no alcohol). We took it to our attorney, who researched the copyright laws for us and followed it through with the attorney for the NFL.
The copyright laws say that you cannot show their copyrighted material on a screen over 51 (or 55?) inches (even if you aren't charging) UNLESS you are a bar, in which case they allow it. So a theater that regularly serves alcohol is okay.
Churches that do this are also in violation. You might remember about 4 or 5 years ago when the NFL went on a little rampage and cracked down on churches and theaters like mine for showing MNF games for free.
Also, even though we were personally speaking with an NFL attorney, we were not able to be granted permission to show the games.