Kosher LA near Centruy Plaza
You are close to the restaurants on Pico leess than 2 miles according to Google Maps - some of my favorites include:
Pat;s Restaurant - an excellent steak house - http://www.patsrestaurantandcatering....
Jeff's Kosher Sausage - some of the best hot dogs//sausages in the US - http://www.jeffsgourmet.com/
Fish Grill - http://www.fishgrill.com/index.html
Mexikosher - http://www.mexikosher.com/
Pat's is the fanciest of the bunch
there is also ditmas cocktails (the chef/owner was a Top Chef tv show contestant) Milky Way (steven Spielberg's mothers restaurant) meshuga for sushi (great sushi and quite filling-we did take out friday night and for the airplane ride home), gotkosher - takeout and cafe. (they also have delicious pretzel challah-we had chocolate chunk pretzel challah and brought a bunch of loaves home to freeze and serve later)