Subject: "Must see" in NJ, FL & AZ?

We are planning a month in the US in Nov/Dec this year, staying mainly with relatives and friends in NJ,FL and AZ. I'm looking for any "Must-see" places in the areas we will be visiting namely:

New Providence NJ- As we'll only be 3 days here we'll probably have just 1 day in New York, an impossible decision I know but time is short.

Stuart, Florida and Mesa AZ. We are hoping to spend a week somewhere within a 300 mile radius of Mesa! Ideas please! Any suggestions will be much appreciated.

Thanks, Jan Bo'ness Scotland.