You can also try Angelique Cafe - my husband and I go there all of the time for breakfast after we go to the flower mart.
Address and AOL City Guide description follow:
840 S Spring St (at the fork of Spring and Main)
Los Angeles, CA 90014
13.79 Miles Away
Get directions | View map
Pershing Square at 500 S Hill St (0.45 miles away)
From the Editor
The image of the toqued French chef doesn't fit Bruno Hervé, who typically wears shorts and black combat boots, but clearly the legions of loyal patrons don't care about his unorthodox ways. Bruno trained in Normandy, and he is a charcuterie (pork-butcher's shop) master. In addition to seductive pâté coated in parsley and the spicy merguez (sausage), there's a delicious smoked-salmon salad, a stellar cold eggplant-tomato casserole, even a decent cheese plate. Count on lots of double kissing at this casual bistro, especially on the patio, where the French contingent dominates.
You didn't say how far you want to walk.
But my favorite is The Original Pantry Cafe. It's an LA landmark restaurant(80 years) in LA. Open 24 hours a day and your classic American breakfast fare and huge portions. Make sure you order the grilled sour dough toast.