The place you need to go for future reference is the following website: 506sports.com. The site has maps showing what NFL games will be televised in what areas.
In general, the Eagles have a reasonably good chance of being televised in the New York TV market (excluding prime-time games and games against the Giants or Jets) if 1) there is no Giants or Jets TV conflict and 2) the Eagles are reasonably good. Because Philadelphia (and the Lehigh Valley) is so close to the New York metro area, there are a fairly large number of Eagles fans in that region, so the Eagles get fairly high priority for non-Giants or non-Jets TV games when there are no Giants or Jets TV conflicts.
Regarding specific games, the key is whether Fox or CBS has the doubleheader that week and if either the Giants or Jets are playing a home game at the same time as an Eagles game. In the latter case, Channel 2 (CBS) and Channel 5 (Fox) are not allowed to show a game opposite a Giants or Jets home game; that Giants or Jets home game will be the only game televised in the New York market in that time slot. If there is no home game conflict, then the question becomes whether Fox (or in the rare cases when the Eagles play on the Eye Network, CBS) has the doubleheader. The network with the doubleheader can show 2 games (unless the Giants or Jets are playing at home opposite one of the doubleheader games, in which case the doubleheader network can only show the game NOT in the time slot opposite the Giants or Jets), while the singleheader network can only show one game. In New York, the singleheader network will almost always show either a Giants or Jets game (if one of those teams is playing on the singleheader network) or a game not in the same time slot as a Giants or Jets game.
I realize this is after the fact, but I'll use the 10/9/16 NFL schedule as an example. That week, the Eagles and Giants/Jets schedule looked like this:
1 PM: Eagles at Lions (Fox - singleheader network)
1 PM: Jets at Steelers (CBS - doubleheader network)
8:30 PM: Giants at Packers (NBC - national broadcast)
The Eagles were not playing opposite a Giants or Jets home game, so Fox/Channel 5 could have shown a 1 PM game (and I'm reasonably sure the Eagles/Lions game was the featured 1 PM game on Fox that day). However, the Eagles were playing on the singleheader network, meaning Channel 5 in NYC could only televise one game. Because the Jets were also playing at 1 PM, Channel 5 did not want to televise a 1 PM game opposite the Jets game - that would be ratings suicide. To avoid that issue, Fox/Channel 5 televised Fox's 4:05 PM game, Falcons/Broncos, which did not have a conflict with either the Giants or Jets.
Incidentally, you can determine which network is the doubleheader network in a given week based on the late afternoon game start times. The doubleheader network's late afternoon game(s) will start at 4:25 PM, while the singleheader network's late afternoon game(s) will start at 4:05 PM.
Hope the above information helps.