Well, I live in Denver now, spend as much time as I can in the mountains, lived in both Seattle and Boston for years, but as a former New Yorker, I still love visiting the city. Yes, San Francisco is great, but like all great cities, they each have a unique character. There are endless things to do there, the food is great, holiday time is beautiful. It is certainly expensive (as is SF). I have the advantage of a brother in law with a luxury apartment on Central Park West, but I can make a couple of hotel recommendations- if not specifics, some generalities.
I highly agree with avoiding hotels in midtown. Look for smaller hotels on the East side, West side. There is a place on the upper west side (sorry, can't remember the name, but will try and find it for you) that rents small apartments, great for families. There is also a Comfort Inn just off of CPW on (I think)71st that has very small rooms, but is reasonable and in a great location (5 minutes to the Museum of Natural History, just across the park from the Metorpolitan, 5 minute walk to Lincoln Center, a couple of minutes to both the A and 1 subways). You may be able to find good deals since your dates are after New Years and the peak season. We got a great deal there a couple of years ago when my brother in law had other visitors, and we were able to get 2 rooms, one for us and one for the kids, at a reasonable (for NY) rate in mid-winter. I have had good luck with both expedia and tripadvisor, but you have to be lucky- sometimes their deals are no deals at all, and dealing directly with the places may be better. Also look at the Hidden guides- they have been good for California in my experience, and I expect their other ones are good, too, for advice about out of the way places to stay that you might not ordinarily find.
Have fun and good luck! And don't forget to stop at H&H on Broadway and 80th for the world's best bagels.