NYC:
I second Maman's suggestion of the Frick. It's a beautiful collection, but small enough that you won't get "museum'd out" before you've viewed everything.
Also, visit the Morgan - Madison Ave @ 36th St. Amazing library (including 3 Gutenberg Bibles), study, rotating exhibits, and a restaurant. (They offer a "Three Martini Lunch" - three mini martini glasses with either gin or vodka - one with a lemon twist, one with an olive, and one with a tiny onion. The glasses are so cute
)
Browse through the Fifth Avenue stores, especially Tiffany. At Tiffany, skip the main floor (always jammed, especially near Christmas) and head upstairs and browse through the engagement rings, silverware, and table settings. (Side note to any ladies who have Tiffany engagement rings: Go up to the sixth floor (repairs, restringings, and such) and they will clean your engagement ring for free.)
Be VERY careful if you go to Rockefeller Center to see the tree. Last year, my elderly mobility-impaired father nearly got trampled more than once. It's also prime grounds for pickpockets and purse snatchers.