Budget things to do when in New York
Visit the outside of the Friends Apartment in Greenwich.
https://goo.gl/maps/ACJ5rAALs142
One that i missed out on which I wasn't impressed with was the Fire Station used in Ghostbusters.
https://goo.gl/maps/TnCjWRssmkm
The High Line (raised park / walkway)
https://goo.gl/maps/3AgDTas1xnG2 Nice walk across the west of New York down to the Trade Centre.
'Pebble Beach' in New Jersey
https://goo.gl/maps/dKQEm5EkBvJ2 Simply for the views of Brooklyn Bridge and the business district.
As mentioned as well Central Park.
Flat Iron Building south of Times Square (didn't get the appeal of Times Square myself)
https://goo.gl/maps/EwY3buNM7cU2
Guggenheim Museum (personal favourite of mine)
https://goo.gl/maps/723kM3sBmiE2 Didn't think much of the exhibits but the building is stunning
(£30 or so to get in though if i remember and take a walk around)
^^All free
Views - Trade Centre, Empire State and Rockefeller Centre all have passes to get to viewing decks. I got a Day and Night pass for the Rockefeller cos i heard the security guys in the other two are stricter and dont allow professional equipment up there. All of them do have scanners in place for obvious reasons though.
Flynyon as i mentioned previously ($499 per person for half hour in a chopper held in by a harness and no doors) Amazing experience but a bit pricey.
I took in a basketball game as well but doubt your missus would want that as a treat on her birthday!
I stayed at the Jewel Hotel
https://goo.gl/maps/MPi2XWqTPbB2. Nothing overly fancy (think i had the view of an office block getting a refurb when i was there) but next to the Rockefeller (handy for the day / night pass) and quite central however if you walk places, you'll be walking for a while! Hotels with a view tend to be hotels with a pricetag to match though so you'll be looking at the more deluxe suites.
Spending money wise, I took £750 but brought back over £300 as I was mainly just buying food since I'd booked most activities in advance. I think all in I was just under £2500 but that was on my own. Bonus on the way back though i got upgraded to first class cos the tv wasn't working on the longer leg room seat!