I am sure nobody will remember it, but there was a place downtown LA that my grandparents would take us when we visited. It was called Chep's (Deli?). Anyways, you sit down and they bring out plates of pickles. Then, we would order 'The Ring Dinger". This was probably a $30 sandwich or so. They would bring this giant platter that had a huge rye and turkey/pastrami multi layered sandwich all cut up with toothpicks and olives, pickled onions and good mustard and whatnot. It fed 6 people more than comfortably.
That said, good LA pastrami sandwiches are almost a dime a dozen there, and I would put 'em up against anything on the East Coast or Montreal, etc. 'The Hat', a chain makes a very passable sandwich that you can find all over. I have found that for some reason, the prices of these types of sandwiches carry a premium that I personally feel are unfounded.
Beyond pastrami, (a pinch of salt thrown over my shoulder to ward off bad voodoo for even saying it) I am mostly excited about Vietnamese Bahn Mi.
Bahn Mi can generally be found in any Vietnamese restaurant, though the trend nowadays is that there are Vietnamese "Deli"s that pretty much do only Bahn Mi, or at least specialize in it. The approach is interesting. The toppings and varieties in these places that specialize are staggering. I would suggest you first go and have one with something you can wrap your mind around, then explore without hesitation the odd and wondrous varieties that they come up with. My favorite at my local place is a baguette, filled with cilantro and mint, pickled daikon and bean sprouts, carrot, hot peppers and then a meat loaf like liver pate, a headcheese type offering, and barbecued pork. I get a side of fish sauce for dipping it into.... Godly stuff. Another hallmark that I appreciate is that the sandwiches are usually $4-$5. I can also get a "double meat" for $2 and easily split one with my wife to share. $6 take out lunch for 2? Yes sir.