Insect bites (e.g., mosquitoes, sand flies, or fleas): The patient's presentation of itchy bites on the thighs, buttocks, and back of the neck, with new bites appearing daily after visiting a beach, is most consistent with insect bites. The location and the fact that the bites are itchy without systemic symptoms support this diagnosis.

Bed bug bites: Given the appearance of new bites daily, bed bug bites are a possibility, especially if the patient has been in a new environment or has recently traveled.
Chigger bites: Chiggers are small, six-legged mites that can cause intense itching and are commonly found in outdoor environments, which fits the patient's recent beach visit.
Flea bites: Flea bites can also cause itchy lesions and could be considered if the patient has pets or has been in an area infested with fleas.

Lyme disease or other tick-borne illnesses: Although the patient presents with bites and not a typical "bull's-eye" rash, tick-borne illnesses can have varied presentations. Given the location (Long Island, New York) and the potential for tick exposure, it's crucial not to miss this diagnosis due to its significant implications for treatment and prognosis.
Allergic reaction or anaphylaxis: While the patient currently has no systemic symptoms, monitoring for signs of a severe allergic reaction is essential, especially if the bites are from an unknown or potentially dangerous insect.

Ectoparasite infestation (e.g., scabies, lice): While less likely, ectoparasite infestations can cause itchy lesions and should be considered, especially if the patient's condition does not improve with typical treatments for insect bites.
Leishmaniasis: This is a rare possibility in the United States but could be considered if the patient has recently traveled to endemic areas. The presentation would typically include systemic symptoms and skin lesions, but it's a diagnosis that should not be overlooked due to its severity.