I can't give you a suggestion for a place on the UES. However, Sarge's Deli, open 24/7 delivers all over Manhattan.
I highly recommend the superb pastrami. Be sure to request it "fatty." To avoid a soggy sandwich, I order the pastrami and bread separately, i.e., x lbs of pastrami and x slices of rye bread, depending on how many people you are feeling. Their cole slaw is excellent. And don't forget the mustard.
I love the sandwich combinations at Gracie Mews, 81st and First Ave.
also try - Peter's at 83rd/84th and First Ave.