Many restaurants that are open for New Years have a special fixed-price menu that usually includes all you can eat or several courses, champagne, entertainment, etc. This builds up to mightnight, when the fireworks go off and everyone goes out with their champagne glasses to celebrate.
At least that's how its been done in Puerto Madero for the last few years.
These fixed menus are pricey tho. Some nicer restaurants here in PM chage $400+ per person. The have these for X-mas and New Years. We've done a couple in the past, but now enjoy the celebaration from our place.