Pink's and Philippe of LA
Made a visit to both in December, 2002.
Pink's has great hot dog, but my recommendation would be to stay with hot dog and chili. I also had "Martha Stewart," but there was so much toppings that the hot dog was buried in toppings flavors. They have Nehi sodas too.
Philippe's the Original
Visited this establishment after a visit to the Japanese-American National Museum. The museum, Union Station, and Olvera Street Market are in walking distance.
What a great place and the french dipped beef sandwiches with a side of dill pickles were great. This sandwich reminded me of Mr. Beef's in Chicago. Nine cent cups of coffee make it worth trip too.
Met a person who takes the bus from San Fernando Valley to eat here. This is must visit place when you are in downtown LA.