As a New Yorker, I can tell you that Lisa is right on the money. You definitely do not need to rent a car to explore New York City. There are just so many ways to get around, either by foot, taxi, train, city bus, etc. (you get the idea). You can purchase a Metrocard at any of the train stations in The City and a ride on the subway will cost $2.00 one way.
There is just so much to see and do here. October is a great month to visit. Usually, the busier times are the summer months and the weeks leading up to the holidays in November and December.
I would suggest going to your local bookstore or library and getting one of the those exploring New York books or even going online and doing your homework ahead of time. One good website is www.NewYork.com
. They have a tab there just for visitors and you can get so much information on hotels, neighborhoods, places to shop, restaurants, the list goes on and on. Even being a New Yorker myself, when family or friends come from out of town to visit and want to see The City, I still go online and do my searching.
As for the ethnic neighborhoods, there are so many. A suggestion would be to visit Little Italy (La Mela comes to mind and Ferraro's for the most delicious gelatto) and Chinatown (Wo-Hops for sure). They are both very easily accessible by train (the #6 to be exact) and are practically intertwined. Nearby is Broadway with all of its great stores and Canal Street with some great shopping deals.
Central Park in the fall is not to be missed. If you can book a room with a view of Central Park, you will not be sorry. The park is huge and there's a zoo too. Just walking around there is a treat in itself.
There's also an abundance of museums and the Museum of Natural History with the Rose Planetarium is a nice stop if you are into that stuff.
My husband is also not a fan of the Broadway Show scene (at all) but Times Square is something you don't want to miss, especially at night. With all of its lights and sounds and things going on there, you can see why they say it is the "City that never sleeps". It's a great experience.
Another of my favorite things to do is just walking up and down Fifth Avenue with all of its terrific shops and then stopping at Rockefeller Center. I'm not exactly sure when ice skating starts there, but that is a nice treat as well.
There are so many cafes and restaurants throughout The City and just places to explore.
Whatever you decide to do, I hope you and your husband have a wonderful trip and enjoy yourselves. The City will be waiting to welcome you!!!