I moved to Brooklyn about 10 years ago, I am still finding new stuff to shoot every week. If you want the touristy stuff there are plenty of iconic sights to shoot, the Flatron building, the empire state building freedom tower. I would suggest if you want a good cityscape to go to Brooklyn bridge park at night, great views of the Brooklyn and Manhattan bridges with the city in the background. Also Liberty state park you get a great shot of the city with the empire state building and freedom tower. Sunsets from battery park, Govenor's Island, or the Staten Island ferry to get a good shot of the Statue of Liberty. If you want to shoot graffiti there is an app called GSA new york that tags graffiti on a map, and shows you a snap shot.
As far as the tickets to sites like freedom tower buy them as you go in-case you find something that interests you and you run out of time. I like top of the rock (rockafeller center) for views because you can see the other landmarks and it is all glass so the view is nice.
What ever you do I would suggest google maps to navigate it will tell you what subway to take and what station to get off at, plan ahead and the subway isn't that terrible to get around and its cheap. Someone above mentioned the Highline, great views of the city from within, food and nice atmosphere, I would suggest going early in the day because it gets busy in the afternoon and evenings. A good bad weather stop is St Patrick cathedral, you can shoot inside as long a service is not going on, amazing architecture
Always have a backup plan incase what you want to do is crazy busy or weather takes out you plans. Google free things to do in NYC too
If it rains go out as soon as it stops as you can shoot some great reflections shots in the puddles.
one last thing is to look at the website "meetup", you enter your interests Like photography and it suggests groups. I go out with several groups and have had a great time following someone who knows the area.