She's a lucky girl ...
Madame Tussaud's on New Years Eve day might be a problem / hassle as the City begins to cordon off the entire Times Square area early -- beginning the day before I believe. I suggest you email or call Tussauds to see what's the deal there.
The boat ride on the lake mid-winter with the rubber dinghy could be hilariously romantic (why hasn't Woody Allen thought of this?). But you might want to think of a "Plan B" just in case it's freezing cold and the lake is frozen over (DON"T suggest that you attempt to enter the lake if there is ice).
There is a great old wooden structure on top of a promontory near the 6th Avenue / Central Park South entrance that would offer protection from th eelements if the weather is nasty. Or the Castle above the Great Lawn has a small covered area, too.
Keep us posted ... Pictures would be great