For just under 9 euros we can go get a day pass for the metro and buses to get around or just pay as we go along which could suck, who knows?. Tommorow we will need to go get our week pass which is much cheaper at 15 or so euros.
We could go and get our Paris Museum Pass (which we can buy at any main metro station or at the Louvre) and then do The Best of Paris in One Day Frommer's walking tour (Map here and Description here) which includes the Louvre, Notre Dame, the Champs Elysee and Arc de Triomphe and then the Eiffel Tower. I say we dont actually go in the Louvre and do that on one of the two days it is open late, Wed or Fri (9am-9:45pm). Instead we just do all the walking around, probably not in that order and first see the Champs Elysee and the Arc de Triomphe, then eat lunch (maybe at one of the UBer neat places that are supposed to be nearby), then head to Notre Dame and walk around more, then watch a free concert at 4 or 5, then eat dinner (maybe at the vegetarian place near the one church) and then go end up near the Eiffel Tower. Ideally anyway :D We can also eat near the Eiffel Tower.. Cafe Constant is cheap and near Le Violon d'Ingres...
Another option is skiping Notre Dame for now and heading for "The Paris Art Market" which according to Frommer's: is "the place to go" on a Sunday. At the foot of Montparnasse Tower, this market is like an open-air gallery and has done much to restore the reputation of Montparnasse (14e) as a quartier for artists. Some 100 artists participate, including painters, sculptors, and photographers, even jewelers and hat makers. Head for the mall along the boulevard Edgar Quinet for the best work. Go any time on Sunday between 10am and 7:30pm (M�tro: Montparnasse). This probably doesnt happen if its raining. We may not see much anyway if its raining that day.
Here is the Frommer's info on those free concerts at 4 or 5 pm that might be nice to see if there's time:
"The American Church in Paris, 65 quai d'Orsay, 7e (tel. 01-40-62-05-00; M�tro: Invalides or Alma-Marceau), sponsors free concerts on Sundays at 5pm. You can also attend free concerts at Eglise St-Merri, 78 rue St-Martin, 4e (tel. 01-42-74-59-39; M�tro: H�tel-de-Ville). These performances are staged with variables based on the availability of the performers, Saturdays at 9pm, and again on Sundays at 4pm."
For the evening we will have to bundle up and head to the Eiffel Tower for any New Years celebrations, though I suggest before then we either make some new friends or locate a newspaper that we can read and attempt to find some kind of party for sure.
Or we can do whatever. Here is a list of things open on Sunday. A star (*) denotes places that use the Paris Museum Pass. (6 days, 60 Euro = $75.68):
*The Louvre: 9am-6pm
Basilique du Sacr�-Coeur: 6:45am-11pm
*Arc de Triomphe: 10am-10:30pm
Tour Eiffel: 9:30am-11:45pm. Fall and winter, stairs open only to 6pm.
*Mus�e d'Orsay: 9:30am-6pm
*Cath�drale de Notre-Dame: 8am-6:45pm (Treasury 2-6 pm)
Cimeti�re du P�re-Lachaise: 9am-5:30pm
H�tel des Invalides/Napoleon's Tomb: 10am-5pm
*Mus�e Rodin: 9:30am-4:45pm
*The Panth�on: 10am-6pm
Mus�e du Vin (Wine): 10am-6pm
Mus�e de l'Erotisme: 10am-2am
Maison de Victor Hugo: 10am-5:40pm