It's really sad thet they care not a bit at JFK, no public viewing area, no terrace, no nothing. Instead: Security watching you.
I just went there today, the customs building is technically OK, I got great shot of SSC departing and arriving, both between 9:00am and 9:20am.
The best place (and easiest) for the Concorde is the BA terminal (8 or 9) where it is parked directly next to the road and you have an elevated position so no fence obstructs your view. Today there was a (charter?) Concorde leaving at around 11:30am, so another opportunity for good shots.
On Saturdays there is also the AF Concorde parked near Terminal 1 during the whole day, you can get good pictures next to the building through the fence!