Today Tix is a great app (download the app or use the website) for getting good deals on Broadway shows! You can also sign up for lotteries and rush tickets through the app. You can also just visit the TKTS booth (different company) in Times Square if you want to take a gamble on what's available for discounted prices.
Everyone knows of "The Met", but most out of towners are unfamiliar with the modern art extension down the street on 75th and Madison, the Met Breuer. They have different exhibits and installations, all in the "modern" era, and it won't take up nearly as much of your day. Plus you could stop by Flora for a bite - the food is delicious and the windows/architecture are beautiful. Entry is donation based! $5 is all you need to pay at any museum in NY to gain entry.
Beautiful views and gardens in this "above ground" park in Chelsea.
This is a no brainer. The park is very large, so if you've never been or are not sure which part of the park you want to explore, check out the map and the website. You can do a carriage ride if you want to fork over the $$, but most of the park is easily walkable.