If you're willing to pay, you can get a late check out no problem

With a 7:15 TATL flight, I'd probably want to leave Manhattan around 3:30 (but I like being there early, relaxing in the lounge, etc) if flying ex-JFK. If flying ex-EWR, maybe 4pm if taking the train (although given DL in your profile, I'm assuming JFK)

Worse case scenario, you can always leave your bags at the bell desk & enjoy the city and pick them up later.