Williamburg and Greenpoint are home to some of the best restaurants in NYC. Look up best restaurants online and try some out, I promise you won't be disappointed. Just make sure you reserve in advance, popular spots can book up early.
Park with amazing views of Manhattan. You can get tacos/bevvies at Tacocina, watch the dogs at the dog park, play volleyball, or sit and look at the views.
Another lively park with way more space for activities. You can go to the McCarren Park House for snacks or just spend time in the grass.
An amazing food festival in Williamsburg. Takes place on the water front with great views and awesome vendors. This would be my number one recommendation for Saturday afternoon prior to the wedding. (Only open on Saturdays.)
Check out the NYC for FREE Instagram page the week before flying out. They post all of the free activities for that week on their page. Theres always a festival or activity happening. I made some suggestions below, but there is truly no limit for things to do in NYC.
Highest outdoor skydeck in the western hemisphere (according to their website.) But I have been and can confirm that the views are insane.
In another part of Brooklyn, but I have heard amazing things. And based on the time of year, you may even catch some cherry blossoms.