Are you driving up to L.A., or staying in Anaheim?
If you're going up to L.A......
I'm a big proponent of the Farmers Market (not just any farmers market, but The Original Farmers Market on 3rd Street and Fairfax in L.A., right next door to The Grove), suggested by SMD above. It's a part of L.A. history and it has a fantastic array of all types of food, all sorts of cuisines, counter service and table service, from both family-run businesses that have been at the Market for decades (Magee's, for example -- great for corned beef), and newer, more contemporary restaurants such as Marmalade Café and Short Order. Du-par's has been there since 1938, and they are known for their pies. Patsy D'Amore's Pizza has been in the Market since 1949. Places like Bob's Coffee & Doughnuts and Littlejohn's, for example, may seem like just your average doughnut and candy establishments, respectively, but they have been cranking out their doughnuts and English toffee for decades and have perfected them. Charlie's Coffee Shop may look like an unremarkable counter service spot, but it was featured on the Travel Channel's show Burger Land as being one of the places in L.A. with a great hamburger.
Also, Canter's Deli -- another part of L.A. history -- is right up the street from the Farmers Market.