The viral "Erewhon of the Hamptons" — Round Swamp Farm — is reliably closed Sunday and Monday at all three locations (East Hampton, Bridgehampton, Montauk). Your Hamptons leg is exactly Sun+Mon, so you'd miss it.
The fix: A curated list of Hamptons-grade alternatives that ARE open Sun+Mon — starting with L&W Market (Almond's prepared-food shop, your best Round Swamp replacement) and Citarella Bridgehampton. Plus sit-down restaurants for Sun dinner / Mon brunch. Everything below has confirmed Sun+Mon hours via Google Places (live data).
Grab-and-go gourmet — for Topping Rose room dining, beach picnics, or the drive back to the city.
From walking-distance brunch to Sag Harbor dinner spots — ranked by priority for your Sun+Mon stay.
Search Google for any Hamptons restaurant, market, or cafe and add it to your list. Photos, hours, and ratings auto-fill from Google.