Bridgehampton Inn has a constantly evolving menu, with new selections offered every two weeks based on local market ingredients. Brian Szostak, the chef, would be happy to hear from farmers and boutique growers about fresh, available items. O’Murphy’s restaurant and pub at the Tipperary Inn in Montauk has a $24.95 dinner special Sundays through Thursdays starting at 5 p.m. It includes soup or salad of the day, a selected entree, coffee, and dessert.