Chow between UCLA and LACMA?
You can have a tasty and very inexpensive dinner during the happy hour at Palomino, on the ground floor of the office building on Lindbrook, one block east of Westwood and a block north of Wilshire. Bar food such as fried calamari or shrimp are half-price, and pizzas from their woodburning oven are $5.
There are a number of Persian restaurants further south on Westwood. My favorite by far is Shamshiri, others like Flame, there is Sheherzad, and Sunnin for very casual Lebanese. All of these, along with Delphi for Greek, Emporium Thai which has garnered some favorable reviews on this board recently, and a couple of Italian places, are all between Wilshire and Santa Monica Blvd. for a convenient drive east to the museum.