Re: New York City for a day
I have been to NYC many times for a day. I like to take an early train in, walk around with my traveling companion(s) to compare NY experiences, see a matinee program (you'd be surprised by how many early theatre performances, music events, etc. are scheduled) or go to a museum for a few hours, eat dinner at one of the incredible restaurants (budget and location are usually the determining factors) and then get a drink at either an old haunt or a new place I've read about. Take the last train you can to get home and savor the time you spent in this great city.
Go to the "Goings on about town" section of the most current New Yorker to see who's playing at Carnegie Hall, Alice Tully Hall, The Beacon Theatre, Blue Note (whatever type of music you like will have a fascinating venue in New York).
The Cloisters are a great destination, as is the Guggenheim, Brookyn Museum, Cooper-Hewitt National design museum, the Frick Collection.