Dick's Variety is just across the street from Surfland Bait and Tackle. You can get most everything from potato peelers through instant mashed potatoes, beer, wine, Spam, canned chili, Wonderbread, and The New York Sunday Times (the daily Times tends to sell out by mid morning). There's a small deli where you can get sandwiches and things like macaroni salad or a lime or two. The Boar's Head bacon is a best buy. The morning muffins are delicious (and sometimes go very quickly!).
Click here for a Google satellite image of downtown (!) Plum Island with Dick's highlighted.