It likely will continue on to NRT or MAD, those are the two 777 destinations from JFK, though I'm not sure if the MAD turn was summer only. Small chance it could do a TLV run, but those are few and far between. What time is your flight? If it arrives late morning, it will likely turn to NRT for the 1 PM flight.
DL seems to do a bunch of ship repositions between ATL and JFK. I've also had a ride on the 777 and several 763ER's with 97XX flight numbers, all have been ship repositions to get them into place for their next flights.