We dined at Vigilucci's before the show. They have a great Happy Hour menu, and if you sit at the bar you get a free charcuterie plate. The meatballs are not to be missed. Our entire check for three drinks and the appetizers was under $25.
We had dinner ~1 hour before the performance at LeRoy's across the street from the venue. Plan ahead if you want a table or just eat at the bar. Staff are conscientious of play-goers and ensure prompt delivery of food/check.