Dubrovnik & Konavle
I've been to Dubrovnik and the surrounding area three or four times over the years, the most memorable of which was at Christmas time in 2001. The city was almost deserted, apart from the locals, of course, and the atmosphere was so relaxing. Christmas seems to be much less commercialised in Croatia and you can really escape from all the tinsel-y nonsense that overwhelms it back home.
Dubrovnik isn't cheap, but you can find more affordable options in the villages of the Konavle region, such as Plat, Mlini, Cavtat or Molunat. If that's still too pricy, you can always stay over the border in Bosnia and save a fortune. Trebinje is only a 40 minute drive away and has a fabulous relaxed ambiance which you won't get in Dubrovnik at the height of summer...