I don’t know what type of place you are staying in (we rent a house in York Harbor every other year or stay at Dockside Guestquarters which has a kitchen and outside patio) but we go to Off the Boat Lobsters and they will steam them for you or you can take them home to cook them. Very reasonably priced and we will eat lobster multiple times a week.
I have no recommendations for really nice restaurants because we always have a kitchen and prefer to cook or do take out for our large group.
York is lovely. Enjoy your trip and celebration.