As a local, one of the funnest things to do is to host out-of-town guests and to just do the touristy things in combination with local knowledge. Bus tours, museums, food, etc. Do it all. For me, it's stuff I'd probably never do unless pressed to provide entertainment for guests I care about.
So, do the local thing with tourists and retain a focus on a combination of showing off the best elements of being a local; with the wide-eyed enthusiasm of the tourist. As a blow-in to NY, I'd like others to appreciate it too.
Do what the tourists do, but with the locals. Do what the locals do, but with the tourists.