Difficult question... as Penny says, Venice is not particularly cheap. We had a very good meal at the Osteria dalla Vedova, also known as "Ca d'Oro) in the Cannaregio area; however, I do not know whether they will be open at Xmas time. I remember we payed something like 60 euros for two and it was excellent and excellent value for money comparing with some other restaurants we visited..
Trying to find the address for you, I found this link which may be useful:
Listings of where to eat in Venice - Italy - Chowhound. They mention alla Vedova and they basically say what I a telling you, but you could read the other reviews as well.
Enjoy!