(I grew up there, so am somewhat prejudiced.)

LOTS to do ANYtime. The weather should be a consideration for you; what you can or cannot tolerate. And seasons for concerts, opera, ballet. And crowds: LOTS at/before Christmas/Chanukah time, and they can be rejuvenating. We went, with kids, every year between Thanksgiving and Christmas.

Also:
The Brooklyn Bridge is not for sale.
Cab rides from the airport shouldn't cost $300.
No one found in the new Times Square is an actual New Yorker.

It doesn't get that hot in NYC, but when it warms up and the wind stops blowing at the end of the day you feel like you are covered in soot.

I have recruited a few DUers to watch my babies, and they are the best.

I was fortunate to have an adult child living on the Upper West Side for several decades, so got in to the city at all times of the year. I've occasionally scheduled a trip just to see a particular play (like Kenneth Branagh's production of Macbeth at the Park Avenue Armory) or opera (Luciano Pavarotti) or concert (Barbra Streisand at Madison Square Garden) or various art exhibits at the Met.

My tip, for an excellent French restaurant near Lincoln Center: La Boite en Bois. In addition to great ambiance & great food, it is also, as the Brits say, good value for the money. You will not see tourists there, nor a smart phone in sight. Diners talk to each other. I have gone there solo a few times - the waiters were friendly and chatted a bit, and the food was so mouth-watering, it easily took up all my attention. Be sure to make a reservation.

http://nymag.com/listings/restaurant/la-bote-en-bois/
http://www.opentable.com/la-boite-en-bois

Located in a brownstone in the heart of the Upper West Side, La Boite en Bois has been a favorite among diners for 28 years. With its rustic ambiance, it feels as though you are in a bistro in the French countryside. In close proximity to Lincoln Center, we offer a pre-theater menu. Serving classics from Escargot to Salmon to Roasted Duck, you will be delighted with our extensive selections. We serve lunch everyday, with a variety of salads, panini, and classic French dishes, such as Croque Monsieur and Onion Soup. Come Sunday for our Brunch, and enjoy Eggs Benedict or Pain Perdu (French Toast). At La Boite en Bois, our attentive and well-trained staff will be sure to provide you with a memorable experience.

And it was a real thrill the year I was in the City for Thanksgiving and we went to the Macy's Thanksgiving Day Parade, which I'd watched on TV since I was a child. We followed that up with a terrific Thanksgiving dinner at The Four Seasons.

The season between Thanksgiving & Christmas is always festive - Lincoln Center with it's classic angel decorations & ice-skating, and the department store window displays - plus it's the height of theatre season, with many great productions - whether you're into musicals or pure drama. The New York Public Theater offers excellent quality plays at a far lower price than Broadway.

There used to be an excellent Thai restaurant nearby - can't recall the name. The people at the box office would know.

It is headquartered at 425 Lafayette Street in the former Astor Library in the East Village section of Lower Manhattan.

The venue opened in 1967, mounting the world-premiere production of the musical HAIR as its first show. It is led by Artistic Director Oskar Eustis and Executive Director Patrick Willingham.[2]

The Public is dedicated to embracing the complexities of contemporary society and nurturing both artists and audiences, as it continues Joseph Papp's legacy of creating a place of inclusion and a forum for ideas.

As you can tell, I LOVE New York. There is an intensity and electricity to the city I have never experienced anywhere else - much as I love cities like Berlin, London, Paris, Prague, Istanbul, etc. If I could afford to live in Manhattan in my retirement, I'd move there in a New York minute. Whenever you go, be assured that there will be a plethora of stuff to see and things to do. A good way to get oriented is to take one of the Gray Line double decker Hop on/ Hop off Manhattan bus tours.

Some where modestly priced but decent neighborhood.

For years I stayed at my dtr.'s apartment on the Upper West Side. After she moved, and when she went back for a visit about 5 years ago, she stayed at the Days Inn at 94th & Broadway, and recommended it to me when I went in to the city about a year ago for a long weekend. The hotel had gone horribly downhill.

The phone didn't work, the cable didn't work, the vending machines had all been removed, the elevators were painfully slow, the wi-fi was "down". No room service or breakfast room. There was some kind of sticky goo on the bottom of the bathtub. No wonder the place had been promoting special low prices on line. Many of the guests were overseas visitors who had been suckered in by said low rates. I was on the go all day long & into the evening with symphony, museum & theater activities, plus eating at great restaurants - so only needed a clean room with a comfortable bed. It never occurred to me that a functional bathtub/shower was not a given. I didn't let the lousy room ruin my trip - I had a great time with all the activities I had scheduled.

So all I can say, is do your research on line for recent reviews by guests. There are still a few travel agents around - I think next time I'm headed to NYC, I'll try using the agent in the office in my nearby strip mall to find an inexpensive place to stay.

Sorry I couldn't be of more help.
Nancy

where in the big city should I stay that is not expensive but close to sights.