I think, in my opinion, one of the most underrated past times in the city is finding a bridge and walking across it. Not only do I appreciate the architecture of the bridge (as I walk directly under its piers) but I also appreciate seeing the city from new angles. It also helps me remember despite how fast the subway system is, that the city is actually huge. You slow down.
So far I have walked across the Brooklyn Bridge (which was alright but touristy), the Triboro, walking across 125th and taking the bridge to Astoria, and the GWB, which you can reach at about 178th I believe.
Here are some pictures. Marvel at how awesome they could have been if they were taken in a decent resolution
GW
Triboro