I live in DC now, but I just moved here from NYC where I lived in Manhattan for 6 years. I am a huge foodie so whenever people ask for recommendations about things to do in NYC I simply send then to where to eat lol
This tour should not be skipped: http://www.scottspizzatours.com/ PIZZA PIZZA and more PIZZA and Scott knows his stuff.
Also best time of the year I would say now like the Fall months (October to mid-November). Central Park is amazing with the leaves turning and it's not too cold. I would not go during Thanksgiving and X-mas as it's EXTREMELY expensive and CROWDED.
Summer is miserable, crowded and hot. Peak travel time. Spring is also a good time to go post-any chances of snow but you might catch rain. So I would recommend April/May and even early June is fine.
Make sure to see a Broadway show. Not sure your style but I've seen tons of shows there and one of my favorites is Chicago. You can get discounted tickets here: http://www.broadwaybox.com/
This site is virtually the same as going to the TKTS office which sells discounted Broadway tickets also, but you can get them ahead of time like weeks ahead instead of waiting until the same day or day before and having to go in person to get tickets.
To stay, I would not stay in Times Square. AVOID. You can visit there if you have never been, but don't stay there. It's rough. Try staying in Midtown East or even Downtown. You will thank me. One of my favorite hotels is The Hudson which is really trendy and fun but tiny rooms. It's in Columbus Circle. More reasonable would be The DoubleTree or the Radisson in Midtown East. Of course there are TONS of hotels in Manhattan. I am not recommending you stay in any of the outer boroughs.
Also get this pass: http://www.citypass.com/new-york Save money, save time, see tons of stuff and have fun!