Things to do in New York
Hiya,
Good to know that you are going to NYC and looking for some offbeat things to do! Regular is boring...so you want something interesting right? I will try my best to give you just the right suggestions!

Brooklyn Bridge at Night, New York City (Source: Andrew Mace)
The city that never sleeps, never bores also!
You can never get tired of this city! There are tons of things to do even after you have covered all the attractions! So here you go!

Sunset at the Rowing Pond (Source: b k)
Since you are interested in offbeat places to eat, dive bars, designs etc, I will focus on those and give you my suggestions accordingly! 
As you probably know this park is not just a New York City landmark. It is more than that. There are some wonderful guided tours around the park. See a list of the tours available here. Customized tours, self-guided tours and guided tours are the three kinds of tours you can choose from. See the calendar here to know the tours available during your stay!
You can either bring your own boat or rent one from here and set sail! The remote controlled boats makes sailing easy even for a beginner! Cool isn't it? See this link for more info and timings.
You can also rent a rowboat for US$12 from Loeb boathouse (10.00 am to 5.30 pm).

Central Park (Source: Erik Jaeger)
- Dive Bar, Dive 75, Broadway Dive are located in 3 different locations, but has the same food. Check out this site to know their address and menu!
- A quick glance at yelp will tell you that Rudy's is fairly popular! Here is a review from New York Magazine:
I visited Rudy's three times during a 7-day vacation in NYC. For me, the best time to come is between 11 am to 1pm on a weekday when there's only a handful of what looked like regulars/locals hanging out. It seems that during the late afternoon and onwards, the place gets packed.
(Source: Rudy's Bar & Grill New York Magazine Bar Guide)
- 169 Bar at Chinatown has transformed from a dive bar to a nightclub now!

(Source: Jason Kuffer)
- Cafe Wha? Show begins at 9.30 pm every night. Reservations are recommended to avoid rush!
- Mercury Lounge in East Village stands out from the crowd for its unique experience of hearing live music in an intimate environment!
- Ghostface Killah will perform at B.B. King Blues club and Grill on Friday 22nd October, tickets are $30 on door, $27 advance.
- Parachute is performing at Bowery Ballroom on Monday 25th October.
See a list of other performers here.

(Source: Tuldas Xenophon)
MAD as it is popularly known is very innovative specially if someone has an interest in art or design! One interesting exhibition here is jewelry since 1948! You can also buy some very creative and exclusive pieces from the museum's store.
At Rockefeller Center Christie's is open to public 5 days a week. Simply walk in and enjoy the beautiful and unique pieces of art that are sold for millions of dollars!
While watching a circus show, ever thought how it will feel to hang on the ropes or juggle 8 balls with just 2 hands! Now you can do all that stuff yourself. Learn how to in Trapeze School. A 2-hour lesson on trapeze can cost US$50-US$65.

(Source: TRAPEZE SCHOOL NEW YORK)
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The tours from this company has been rated as a number 2 in NYC. The Goodies Galore tour is the 3rd best in whole of US according to TripAdvisor ratings. See this article to know more! See the site for dates and times of the world famous sweet tooth tour!
Tickets at US$35 per person.
Food on Foot Tour (Source: Daniel Torres Bonatto)