Good morning, Sam. Sometimes overlooked are the flight schools in New Jersey, just over the Hudson River from Manhattan. They would be less expensive, and easy to reach from Philadelphia if you chose to go that way from LHR rather than New York City.
Near Morristown N.J. is the ATP Flight School. Or in a quiet area, Freeflight, Medford N.J. And if aviation history interests you, the historic Lakewood, where the airships used to anchor after their transatlantic voyages, there is a flying school at Farmingdale N.J.
North of Atlantic City where I was born, you will find very nice beaches, quiet resorts, with decent waves and warm water through September.
Enjoy!