Is four and a half hours enough of a layover time to leave Frankfurt International Airport for a quick bite?

I have a very close friend who lives in Frankfurt and it would be absolutely amazing to leave the airport for just an hour or so to meet her and grab a quick bite with her. Maybe we can even eat at the airport itself? I heard somewhere that the airport officials decide whether you can leave the airport or not. I... show more I have a very close friend who lives in Frankfurt and it would be absolutely amazing to leave the airport for just an hour or so to meet her and grab a quick bite with her. Maybe we can even eat at the airport itself?

I heard somewhere that the airport officials decide whether you can leave the airport or not. I understand that I would have to go through customs and all but do you think this is a feasible thing to do?
Update: I am a United States citizen so it seems that I do not require a visa to enter into Germany..
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