The Music Center has three restaurants and two outdoor cafes.
On the Main Music Center Campus, you'll find Pinot Grill on the Plaza and Kendall's Brasserie and Bar at street level on Grand Avenue. You can also grab something quick before a show at the Spotlight Café or Pinot Grill to Go, both on the Plaza.
At Disney Concert Hall, you can choose between fine dining at Patina, or casual dining at the Concert Hall Café.
The Music Center restaurants don't stay open more than an hour after the end of performances, so check my list of Where to Go After the Show for other nearby options.