The only hotel on site is the TWA Hotel, for which I have my first stay in a few weeks - I have visited during the day. Like the Sofitel it's incredibly convenient, and if you are paid in sterling incredibly expensive. My other hotels - and there are lots - are the Hilton Garden Inn at JFK, which has a shuttle and you can use the public bus service Q10. The Hilton is a bit further away but has a more regular shuttle service from Federal Circle than other hotels and if you think you've waited too long for one they will send an extra shuttle round to you. You could also consider staying nearer Manhattan since you should have time for an evening in town.