Austria trip in winter?

My GF and I have a chance to buy tickets to the Vienna New Year’s concert - not the televised New Year’s Day performance but the day before, I believe it’s the same program. We’re still trying to decide if it’ll be worth our money and time to go. A few questions:

[ul]
[li]I tried to look at a couple of hotel web sites and they didn’t show any rooms available for the end of year. Is it possible they are sold out already, or are they not accepting reservations yet? I could ask individual hotels but I wanted to get some sense of how far in advance decent (~3 star) hotels sell out for holidays.[/li][li]Roughly speaking, how much should we budget for a week’s stay in Vienna + Salzburg over the holidays, with ~3 star hotels and restaurants? (Excluding air fare and concert tickets, which we already know about.)[/li]In general, is that a bad time to visit there in terms of sightseeing (and cost)? (One week around New Year to be exact, not including Christmas.)[/ul]