If you want to present a thing, which would be really a desired one, you should know for sure what the person wants...
Of course, you can ask him/her directly what she/he would like to get for the New Year, but in this case there won't be surprise. That's why one of the best ways to find it out is shopping with this person. You should ask your, say beloved, to make shopping with you, and when going along shops ask him/her different questions about the thing you see in shopwindows or on counters.... Make notice what she/he likes and what pays attention to... Moreover ask him/her leading questions and you will know about the desired present for sure!!!