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Pretty much all the restaurants will be open since Christmas is not a holiday in Indonesia. I've spent Christmas in Bali twice (once in Kuta and once in Ubud). Hotels have great (but expensive, relatively speaking) dinners with all the trimmings, but you can sometimes find restaurants which cater to expats that do turkey dinners complete with plum pudding for dessert.
If you arrive in Ubud before Christmas, just wander around the town or ask at your hotel for information. At least for smaller restaurants, you usually have to reserve, and it's probably the same for larger hotels.
