Oooooh Peter, you and the missus must come to visit my shop in the East Village!
The
New Jersey Transit Northeast Corridor train stops at Newark and runs straight into Penn Station, NYC - it couldn't be easier.
There is so much to do, it's a bit overwhelming. I would make my first stop the
Metropolitan Museum of Art - it is one of the world's great museums. You could spend all three days just wandering the galleries there; seriously, don't miss it.
In addition to the
Guggenheim already mentioned there's
MOMA (if you're fond of 20th Century art, it's the place to be). The
Whitney Museum of American Art also has a fantastic collection. The
Cooper-Hewitt National Design Museum is a wonderful little collection, and there's the
Morgan Library and the
Frick Collection as well - these are all incredibly well-curated collections housed in the great turn-of-the-century mansions of America's "royalty."
The American Museum of Natural History is always fun, and there's the
Neue Galerie - a fantastic collection of early 20th Century German and Austrian Art that also houses a fantastic restaurant. There are so many more, like the
Tenement Museum in the Lower East Side, which is a wonderful little museum that lets you step back in time to experience how many of New York's immigrants lived at the turn of the last century. The
International Center of Photography is a wonderful, wonderful museum as well.
For the History of New York I wouldn't miss the
New York Historical Society, just a stone's throw from the Natural History Museum.
Don't miss a stroll through
Central Park, Fredrick Law Olmstead and Calvert Vaux's green masteriece in the heart of the city. It is a popular migratory stopping-place for birds of many species (being the largest swath of green in the area) - fantastic bird-watching. Autumn in Central Park is one of life's great pleasures. Many of the above museums are on 5th Avenue (museum mile) which borders the park, so it's a very pleasant day or two of wandering.
As for restaurants, there are just too many to mention. I know some wonderful local ones I would recommend.
Feel free to PM me - I've been directing visitors around the city for a long, long time.