If I remember correctly 2nd Ave Deli was at one time Kosher, but later decided to drop it in favor of being open on Saturday. Carnegie, Sarge's, Stage and most of the "Jewish Style" Deli's will serve milchik with fleishich.
When I was around 17 I walked into the deli where I lived with my first shiksa GF. She ordered a corned beef with swiss cheese...... and they gave me a dirty look.