To have the best lunches like a 'fried peanut butter sandwich', lounge or book a room for a few days in the heart of the city, visit 'The Ace Hotel'. Ease down in the couches, order a Brooklyn Beer and relax. A great place to meet up.
The best underground shows you will find will have free pbr and models as far as the eye can see. They are rarely announced, so keep your eyes out for promising openings, especially with Milk Underground coming up.
When I first visited NY in 2010 the New Museum left a permanent impression. I love the architecture and the concept of the piled-white-shoe-box look-a-like building at the edge of the Lower East Side neighborhood. The exhibition program is appealingly different, and the bookstore in the foyer is not to be missed!