I don't celebrate Christmas, and when my kids were young, I tried to deal with Chanukah in a way that didn't totally give in to the gift giving frenzy of the season. Also, when they were very young, we lived in a place where the Jewish community was small, but growing, and not everyone my kids met understood why they didn't have a tree (those poor deprived kids!). What I decided to do, was given that there are 8 nights of Chanukah, we chose one larger type gift to give them on the last night. Two of the nights were taken up with presents from each pair of grandparents. The first night we gave them a small toy. For the remaining 4 nights, we did things like candy, a family outing to children's theatre, a movie, books, or getting together with friends. As they got older, they volunteered to give donations to various charities, as part of the celebrating. My DH and I have never exchanged gifts for Chanukah, as our anniversary is 12/8 and we are more likely to do something for that.
This year, for the first time, we are going to our older son's house to celebrate tonight. We bought them a pair of artist designed wine glasses at a local artists' co-op, and are also giving them 2 bottles of wine, as well as a scarf for my DIL, that DH brought back from one of his trips to Asia. My other son and his wife are visiting the week after this one, and we got him a very nice Mountain Hardware shirt and her an artist made leather clutch, from the same store where we got the wine glasses. We also are paying for their rental car when they come to visit.
I send my dad a gift basket of some type of food or a gift certificate to a store.