Flying from JFK (Would only consider Newark if the fare was several hundred lower per ticket - which it is not)
If you want to fly direct the only options are Delta (JFK), United(Newark), and ElAL (Both)
I flew last summer during end of june beginning of July - $1398 booked May 9th, that was the cheapest flight at that point could have been cheaper booking a little bit earlier, if i remember correctly delta at that point was the most expensive of the three