Comic Strip Live- If you don't feel like paying Broadway prices this place is a great choice. This club always seems to put on a great show, we had a blast the last time we went and across the street is a little dive bar that is a lot of fun to hang out afterward. I went with three other people and all four of our tickets were $40 so definitely a discount from $200 Broadway tickets. You can usually buy them off a street vendor, they'll have some sort of sign or they'll approach you.
MoMA- I actually never went to this museum while living in NYC but I have plans to go during this visit. I've heard its amazing. Target Free Fridays get you in for free from 4-8pm every Friday night.
The High Line- This is such a cool place in NYC. It lets you escape the craziness that is NYC for a little while and there are some really awesome buildings to look at on the walk. This is actually really close to a lot of great places to drink and eat as well.
Guggenheim- This is probably my favorite museum in the world. I'm a huge fan of impressionist and post-impressionist artists so you can probably see why. The last exhibit I went to there titled Haunted was chilling yet beautiful and presented in a way that the viewer appreciates. My dad is a huge fan of Frank Lloyd Wright who designed the building so I'm excited to take him there to appreciate it in person.
Staten Island Ferry- If you want to get a great view of the Statue of Liberty but don't want to make the trip out to Ellis Island this is the way to go. The ferry is free and departs every 30 minutes. It takes about an hour round trip and literally passes right by the Statue of Liberty.