I agree with Norma, Bets, and the rest. (And Karen - hah! Excellent comment! As for you noale.berger... great idea! Never heard of it. Thanks!)
Stay in Paris. It is ENTRANCING over the New Year's holiday. And romantic?! Fuggedaboutit! Sooooo romantic. I encourage you to skip the side trips and just concentrate on the most beautiful city in Europe (IMHO) when she is all dressed up in tinsel and colorful flocking and magical lights.
Hang out at the wonderful Christmas market along the Champs-Élysées: it's chockablock with stalls hawking gifts, local cheese and sausages and savories, roasted chestnuts, warming delicious mushroom soup, and hot mulled wine. Take in the light show on the Eiffel Tower - it happens every night, starting at dusk. The perfect place to watch is from Trocadero, looking over the river.
If you like shopping, the "grands magasins" (Galeries Lafayette, Printemps, etc.) are all spectacularly decorated for Christmas and well worth a visit. Actually, at this time of year, there's hardly a shop that isn't gotten up with cheerful decorations.
And of course there's everything else in Paris to do... hang out under a cozy heat lamp at an outdoor cafe, people-watching and sipping vin chaud... stroll along the Seine and check out les bouquinistes... see Notre Dame in her holiday finery.... visit Sainte-Chapelle and marvel at the eye-popping stained glass (or catch a concert)...
As for New Year's Eve itself? NOT "underwhelming." I am sure Amsterdam has a light show. And I know that recently Paris hasn't done "official" fireworks. But it's a huge party all along the Champs-Élysées, or you could head up to Montmarte and get a stunning view of the skyline at night, then go someplace and grab a glass of champagne...
Anyway, that's just me. I love Paris, and visit almost every year at Christmas, so I am partial. :-)