When I stay at a friend’s place, they are on the upper east side, I’d take the subway to Canal and meander routes back to their place. Different day, different random route. Freshen up for dinner, go out with them as the tour guide.
I like wandering the streets, stopping at a 3-card-monte game, interesting gallery, store or what ever caught my eye. Easier if the weather cooperates. Allows the thrill of a discovery and a pace not hurried by an agenda. There is so much to see, I would be hard pressed to pick any one as a must see.