Hi,
Vienna is a great place for christmas - so congratulations. You will have an awesome time, I suppose.
The weather will be cold - not Russian cold, but well below 0 Degree Celsius. So you will want to pack some warmer clothes.
Vienna is famous for its coffee house culture. Its great cafés, etc. You will want to catch this vibe - sit down with a few newspapers in a café and relax. It'll be nice.
I'm not sure what to recommend exactly in terms of sightseeing, as I do not know the city too well. You'll probably want to check out the homepage of Vienna.
Best regards, Bjoern