I'm going to list some of my favorite sandwich places in NYC. All of these sandwiches are not cheap, and start above $6. If you want something cheap or something that is more of a traditional sandwich, the $5 footlong at subway really is a good deal. I usually get the banana peppers to add flavor without adding something cream/fat based. This list is by no means comprehensive, but I'm at work now with nothing to do so here goes.
http://lamazoucheese.com (3rd ave/27th st)
Lamazou is a small cheese shop that has a large selection of premium quality meats and cheeses. Almost every sandwich there is good. I tend to have my sandwich on their ciabatta, but I also listen to their suggestions as they seem quite knowledgable. My favorites are the 1. Smoked Salmon with Lemon dressing, Capers, Onions, Cornichons, the 4. Mortadella, Salami with Provolone cheese (must add roasted red peppers, this sandwich becomes amazing) and the 21. Chicken Salad, Cheddar & Sundried Tomatoes. Another great thing there is their roquefort egg salad. Yes, egg salad mixed with a good amount of one of the tastiest blue cheeses. Fattening for sure, but oh so good.
http://baoguettecafe.com/index.html (Murray Hill, East Village, West Village)
I will not debate whether this banh mi is authentic or not, and I understand that it's hard to justify the higher price when cheaper banh mis are to be had all over NYC. However, their ingredients are fresh, the bread is nice, and I'm mostly there for the curried catfish sandwich that comes with cucumber relish, pickled red onion, and honey mustard sauce. While catfish is a relatively cheap fish, a fish sandwich for $7 is not horrible.
http://www.numpangnyc.com/index.html (University Pl/12th st)
The sandwiches here are amazing in their variety and the freshness of their ingredients. Whatever needs to be grilled is grilled to order before being put in the sandwiches. Everything on the menu looks good and they have a good array of daily specials that actually change frequently. While the size of the sandwich doesn't look like a lot, the semolina bread is quite hearty and should fill you up quite easily. When I ordered the shrimp and spanish mackerel sandwiches, the portion sizes were good too.