overnight in JFK

Agree with everything.

I always try to get a break in flight outside of US, because they always check your luggage straight to JFK, once had to break the flight in Miami and it was such a hassle.

It will be easier to take them to terminal 3 and check them there, less chances of losing your stuff. You can take the air train to go from terminal 7 to 3 so don’t worry about lugging it all the way.

My personal opinion would be against staying in a hotel, its a whole lot of trouble trying to get the shuttle to the hotel, sleeping, showering and trying to get back to the airport. Would be a lot easier, although a bit uncomfortable to stay at the airport.