The Berkshires is one idea. Here's a very current thread on things to see/do in that area but there's also skiing. Mass Moca and the Clark Institute are terrific museums. http://www.fodors.com/community/united-states/berkshires-in-january.cfm For antiquing, Hudson, NY is loaded with antique shops and the town of Sheffield, Ma has a number of shops in/nearby.

The area around Hyde Park is another idea with a visit to the Culinary Institute for a meal and the Vanderbilt Mansion.
http://www.nps.gov/vama/planyourvisit/hours.htm
http://www.ciachef.edu/restaurants/default.asp
http://www.tripadvisor.com/Attraction_Review-g60801-d253262-Reviews-Culinary_Institute_of_America-Hyde_Park_New_York.html

The Hamptons off season can be quite romantic and much more affordable for some luxury. Ice skating, romantic walks on the beach or through the villages, some nice dinners and some antiquing and some wine tasting at Wolffer Vineyard or Channing Daughters.

There's also good antiquing in the New Hope, PA/Lamberville, NJ area with some nice b & b's although I've not been in a while.

taking a ferry across the sound might be fun--could do Newport or Mystic ( avery romantic spot


http://www.webscope.com/li/ferries.html

You might look into Kent, CT/Lake Waramaug area.

I would recommend Newport, RI for the first choice because it meets your criteria perfectly. Winter sports, museums, antiquing, just everything you want to do. I personally love Newport and have been there so many times.

I also agree with Bigbomoho that Mystic is another option. Though, it's a smaller town. But it's beautiful and a hot spot. Both towns are romantic spots. You'll just love the sunset while standing by the water on the main streets.

How about staying local? Long Island wineries have a "Winterfest" every year with lots of activities and great deals on lodging:
http://www.liwinterfest.com/liwinterfest/?src=liwinterfest.com

http://www.mohonk.com/

Not inexpensive, but if you can go mid-week & get a good rate, Mohonk is a special & romantic as it gets.

Romantic is in the eye of the beholder. A couple of friends went to Mohonk last fall. they said the food was mediocre at best, rooms not very luxurious and not much to do unless you wanted to hike all over the place.

nytraveler, everything is in the eye of the beholder. For those of us who love history and hiking, Mohonk is in a class of it's own. I guess it's possible to go there and fail to appreciate it though... but in dozens of hiking visits and quite a few dinners, I'm always captivated by it's unique charm.

I'm a huge fan of the gorgeous state of Vermont, but not so much in February. Plus it would be the furthest distance for you. Save it for spring/summer/fall.

It depends on what you're looking for. "Rustic" doesn't appeal to a lot of people at all - never mind for a romantic weekend. And I've heard complaints about the food from others.

And as for hiking through the woods in February - when you choice is snowy or muddy - not a chance in hell.

nytraveler, just to correct misperceptions, Mohonk is not rustic. It's the site of many weddings and most would consider the setting romantic. The OP is looking for an active trip, hiking is active as is skiing. This winter's snow has made for great ski conditions. Mohonk has groomed X-C trails and is close to Minnewaska State Park where trails are also groomed. And you've "heard".... well, clearly you've never been there yourself and it doesn't help the OP to pass on rumors. The request was for recommendations. Engaging in discussion with you is certainly not helpful to Titi, as far as nytraveler goes, I'm out.

Titi, congratulations on your new relationship & wherever you go, enjoy your trip! mclaurie has good suggestions for the Berkshires or Hyde Park as well. You might also consider The Beekman Arms in Rhinebeck, just north of Hyde Park: http://www.beekmandelamaterinn.com/