Ironically, I can't give you too many ideas about SF, even though I live 15 minutes from it and go there about 3 times a week! Funny that locals tend to pick up on the smaller things and never get around to seeing what people travel far for
I'll try my best though. The most popular of touristy things seem to be riding the cable car from it's turn-around on Market and Powell through the city, fishermans warf and pier 39 then a ferry to alcatraz for the day, walking through Ghiradelli Square, driving down Lombard Street from the Pacific Heights (the "wind-iest street in the world"), and shopping in Union Square (right off of Market).
Some of my more experienced, "local" recomendations would be:
-Walk or drive across the golden gate
-Above it (if driving) is an A++ viewpoint of the entire bay. Go over the GG north (away from SF) and take the first exit once over and head up the hill on the left hand side. Stop where other people pull over and check out old batteries (retired military bunkers) and check out the view.
-The Exploratorium (if you have kids or a love for fun science) and the palace of fine arts around it (cool greek-looking structures around a man-made but beautiful pond
-Drive over the bay bridge (away from SF) and pull over on treasure island. Drive down and pull out where the car park is to get another great angle view of the city that commonly goes overlooked.
-Eat at the Cheesecake Factory on top of Macy's in Union Square
-Visit NorthBeach (historic Italian section) and eat anywhere that looks good (true italian style!). Steps of Rome and The Stinking Rose (garlic) are the two hottest tourist attractions but really are just as good as anywhere else. Take the bus if possible, parking is horrendous every hour of every day.
-Check out Haight/Ashbury up in the hills.
-SFMOMA off lower Market (sf musum of modern art)
Thats all I can think of for now. And as far as New Years goes, crowds and crowds of people flock to Emarcadero on the water for fireworks. Lots Mainly younger kids (15-30) but definitely safe for the family.
Enjoy my hometown! PM me if you have any specific questions.
-Tim