Everything in New York (except McDonalds) is unfortunately about double what it is in any other North American city also, a great many things will be closed over Christmas. That said:
The Russian Tea Room (reopened in November) on west 57th
Tavern on the Green in Central Park
Fraunces Tavern at 54 Pearl Street (restaurant first floor, museum and offices second floor) although it's principally a financial district lunch spot, it can be fun.
The museums (Metropolitan, Natural History, New-York Historical Society)
The Top of the Rock - Rockefeller Center (in many ways a better view than the Empire State Building - and a LOT less expensive)
Things that you can do on Christmas Day: depending upon where your GF lives a walk around the Battery (tip of Manhattan) and the financial district,
World Trade Center area, a walk across the Brooklyn Bridge (upper level for pedestrians), a walk around Central Park (daytime only), looking at the shop windows - principally Fifth Avenue from 34th Street up to Central Park South.
If you're interested in such things The Cathedral of St. John the Divine
Amsterdam Avenue near Columbia University, St. Patrick's Cathedral
Fifth Avenue, St. Thomas' Church on Fifth avenue north and across the Street from St. Pats (amazing blue stained glass widows)