I would actually venture to say that the alphabet ledges in Staten Island are a worse spot, in terms of being everything that a NY spot isn't, than the Lenox ledges.
Lenox ledges are not worth the trip, but since you're staying a little more than 9 blocks away, you should at least check it out. Skate uptown from Amsterdam, make a right on 110, bomb the hill, look both ways, and the ledges are on the corner of 110th and Lenox.
Beware of Shit Demon. His name is enough for me to tell you to beware. Beware.
Farter east, on Central Park North, there are some more ledges in front of an apt building, but they're usually not waxed. you can be the johnny appleseed and wax them shits, and we will be forever grateful.
There is only one flatbar to skate at tompkins, and the cracks that have developed over the years have been filled in with tar, which melts and makes life awful for the throngs of skaters that try and live there. Avoid it, but buy some limited edish shit at Autumn.
Rohan, the mayor of tompkins, is also currently banished from the for an indefinite period of time over some bullshit. Stay up.
Seriously, though, there are spots everywhere, and most of the best ones are probably not even noticed by the locals. Get a peice of paper and draw a grid. write "uptown" on the top, "downtown" on the bottom, "east" on the right, "west" on the left, and let that be your guide. You will not run out of places to skate, nor will you get lost or end up in some sketchy cut. Manhattan, below 110th, is entirely bougie and totally safe and skatable.