early March in Montaulk
Never the wrong time for seafood out there, there's always something being caught. Montauk is definitely the place for seafood.
Most Montauk restaurants start opening the weekend after St Patricks Day, but I guess you'll miss that. Right now mostly just bar and grill type food; O'Murphys is pretty good and right in the heart of town. Easthampton, not everything is open but you'd have better luck with Asian/Italian (unless you mean take out Chinese or pizza joints, there are a few of those in Montauk).