Sorry, I do not remember the currents at the moment. Will try and look up if you do not get other posts. Eldridge's or Reeds would tell you.
It is reasonably quick once you get through. ? an hour??
Our initial trip through was complicated by having to take the eastern route ( and wait for a bridge) around Roosevelt Island due to something going on at the UN. You may want to double check with the Coast Guard, and the news. If any dignitaries are coming or the UN is in session, you may be routed around. Also, some days they close it all together.
Also, check the mast height vs that of that RR bridge on the East side of Roosevelt Island in case you are routed that way.
There is a little anchoring spot on the east side while you wait for the bridge to open. It is just a quick stop.
It is an exhilarating trip, past the Statue of Liberty, though watch out for the speedy orange Staten Island Ferry and all the cargo ships!
For a place to stay once through:
There is a lovely Yacht club at Great kills off Staten Island, if you are member of another Yacht club, to the right after you get out . Richmond something. Very reasonable mooring balls.Very friendly. A good place to stay the night.
Another option is to Anchor off Sandy Hook, though that may be a bit too far south.
There is also an anchorage in Sheepshead Bay, I believe. to the left.
There may be a quicker route for you further east. I would have to check the charts. There is a cut away by ? Orient Point? I believe, by that Island whose name escapes me at the moment. You need to watch the tides there as well.
Good luck. I am doing all this from memory ( 3 years ago). If you do not get other replies, I can look up the info in my guide books. I do not have a current Eldridge yet.
(WE don't hit the water until at least May in Maine.
Wishing you fair winds and best of luck on the new boat!