re: What are some non touristy must do's in NYC

Depends on where you're staying and when you're going. Not really sure what you mean by "non-touristy," though. You could sit at a coffee shop and scroll Craigslist looking for an affordable apt?

Actually, go get a burger and shake at the original Shake Shack in Madison Square Park. Eat it at the outdoor seating and people watch in the shadow of the Flatiron building. Still pretty touristy but not quite "go to MoMA" or "see the Empire State building" level. And if you do want a high rise view of NYC, go to the top of Rockefeller Center, not Empire State. Much quicker line and equivalent view.