I've eaten at Papa Christos (Greek) prior to going to the WIltern. Its nearby (but not that you'd walk it), and it isn't a "nice dining experience" if by that you are talking about the atmosphere / service -- I like the atmosphere at Papa Christos, but it's the order at the counter, wander through the store, enjoy the cinderblock kind of dining experience. If by "nice dining experience" you are talking only aout the food, I'd say it qualifies.
I've never been, but many people seem to like Taylor's Steakhouse, which is in the area. I know it's a common destination for people going to the Wiltern. I'm sure you can find plenty of threads that discuss it - including ones that feel it has gone downhill.
I always go to Soot Bull Jeep when I'm going to the Wiltern, but you did say no Asian.