There is a cafe right by the Mark Taper, Cucina Roja. There are several high end restaurants at the music center. There is a great vegetarian Vietnamese restaurant across the street from Disney Hall. My wife and I usually eat in the Art District, about 19 minutes or less away - a lot of places to choose from.
Kendall's Brasserie is south of the Taper, below the Dorothy Chandler. You'll need reservations. The Disney Hall has a cafeteria style eating area on the first floor often to the public. Beyond the Broad, there are two more nice restaurants. Many L.A. restaurants will call the downtown shuttle to take you and return you from the theater, saving you the extra parking cost, although the driver's tips either that out.
I don't know but the Theatre is great.
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