While you can kite at these spots almost year round, for real big air and strong winds, spring and fall months when storms pass through are best. During these months on average there will be at least 2 days a month with over 25kts and up to 1 day a month with 30+kts. Weather can be variable with rain, overcast, and gusty conditions during storm periods, but true big air fans should feel right at home in these conditions.
Water and ambient temps are better during the fall months when the ocean and great south bay still carry a lot of heat from the hot summer months allowing you to ride in mostly 3/2s without gloves/booties. Spring months on the other hand are a bit more hard core temp wise and often require 5mm and booties/gloves to ride.
For flat water big-air Tobay beach is the local go-to destination. It offers miles and miles of inland channels and open flat water sections with buttery conditions. The beach is only open to non-swimmers outside of the main summer season.
For waves/kickers gilgo and oak beach give access to the Atlantic ocean side providing both left and right foot forward options depending on wind direction.