"12/4- IAH (prefer HOU)-NYC (prefer JFK). Depart anytime but must be in the city by 3:00 PM"
If, by "the city," you mean Manhattan, why do you prefer JFK?
If you can find Coach "MileSAAver" space on AA
nonstops between IAH/HOU and LGA/JFK at aa.com, transfer your UR points to BA, and redeem for 10K BA Avios each way -- with no close-in award-booking fee.