Yale Club
Used the Yale Club a couple of years ago for dinner one evening when in NYC, did try to book in but the Club was full. Years before I used the Club as a visitor, mainly to use the squash court. Found the Club an excellent place and the reports I have read on the accommodation have all been good. However I expect you will find that all the RAF Club NYC reciprocals will be up to the same standard.
As others have mentioned you will get lower cost accommodation in NYC, but if you want the best, go for it!
Another point, the Yale Club is on Vanderbilt Ave right next to Grand Central Station and you can get the shuttle bus from JFK (and Newark I believe) that terminates at Grand Central. Good service and a lot less than a cab and quick transit (apart from the traffic!).