This is one of my favorite spots in Vegas, and since it's open 24 hours I can go any time I want! Their sandwiches are delicious, the service is quick, and the food is very reasonably priced, too (only $5.99 for a sandwich). It's also conveniently located inside Planet Hollywood hotel just a minute's walk from Fat Tuesday, so you can kill two birds with one stone while you're here.
My personal favorites are the Full Montagu and the Earl's Club. We ended up ordering extra sandwiches for our way back home on our trip there this past weekend, so lucky for me I have an Earl's Club waiting for me at home for lunch!