Frequent NYC visitor thinking about visiting in March, possibly alone. (things to do alone)

Im looking for ideas on where to stay and what to do. I may or may not be alone. If I'm alone I'd like to get some cool ideas of places to visit, things to do. I have never been to brooklyn so I wanna check that out. I wanna checkout the garden on top of the subway rail (name escapes me). Any other ideas on things to do in NYC alone? I enjoy traveling by myself, its relaxing...so relaxing things are always good (even if its just a place to drink a glass of wine with good view of the city or whatever). I'm not new to the city so the tourist shit gets old (times square, statue of liberty, etc)

suggestions on places to stay? I'm thinking ill come for 4-5 days. Hotwire has a hotel for $555 for the time I want to stay so thats not too bad but the cheaper the better.