What do to while in NYC and Las Vegas
 

Mrs and I are going to the states for 4 weeks this Xmas. Almost 3 weeks in NYC, then to vegas for a week or so. 20 Dec to 18 Jan.

Aside from the obvious stuff to do...
NYC - Walking tour, Museums, Buildings, Rangers game if on, Knicks game if on, NYE in Times Square, maybe day trip to Niagara, Broadway show, Seinfeld Diner

LV - Grand Canyon, Hoover Dam, Shooting range (novelty for us, no guns here) Nascar experience, Exotic Racing, maybe day trip out to Death Valley, shopping at that outlet mall

Looking for recommendations for other things to do that you'd recommend.

In NYC we're staying on W 58th, and in LV at the bellagio.

I've been to both places before, but on much shorter trips.

For LV, I'm looking to do this:

http://digthisvegas.com/

There's a lot to do in NYC and since you are there for three weeks you have some flexibility.

The downside is that at that time of year it can be cold so YMMV. To your list, I would specifically suggest:

Walk across the Brooklyn Bridge, One World Trade Center, 9/11 Memorial, The High Line

Hookers

Niagra and Death Valley wouldn't be day trips.
Maybe if you fly from the base cities.
Niagra may or may not even be accessible on any given winter day.
Those are all day drives one way before you can tourist them.