I don't live in New York, but I go there several times a year. The most annoying thing to me, another tourist, is a group taking up the whole sidewalk and then stopping to take pictures. Walk in smaller groups of 2 or 3 and move out of the way if you want to take a picture of anything.
A million times this.
Just try to be aware that while it's a an adventure for you (and it should be! enjoy it!) there are millions of people here who are just trying to get through their day: it's hot, it's too crowded, and they are probably late for a meeting. :p Try to be aware, all the time, of whether you are in the flow of traffic or not. It can be exhausting to have a part of your brain always scanning and taking the people moving by you into account, but it's worth it.
In other words, think of walking in NYC more like driving in most places. You may be out for a relaxing stroll, but most other people are 'on the highway' mentally. That's also a major reason why people don't stop and say hello randomly, or get chatty on the streetcorner - most New Yorkers aren't trying to be rude, they've just got their blinders on and are focused on their objective.
That being said, stroll away in the parks. That's what they are there for.
I think groups of tourists sometimes take up tons of room while walking down the sidewalk because the 'personal space bubble' is a lot bigger other places. So you get 4 people, all with 'bubbles' walking in a group, and it uses up the entire sidewalk. Try to be aware of this and set aside your own personal space bubble when appropriate (most of the time).
Apart from that, I would say make sure you get out of the super tourist areas and enjoy the unique things the city has to offer! Don't eat at a restaurant you could find back home, go for something unusual, one of a kind, or at the very least that you haven't tried before.
The subway runs all night, but it does run very infrequently at 2am, so cabs are more efficient at that point.
Don't give a cabby an address, give him cross-streets. Unless he has a GPS, an address isn't going to help him.
26th St to 27th st is a tiny block. (blocks running north-south) 6th AVENUE to 7th AVENUE is a giant long forever block (blocks running east-west).