what is the best place to go early december in europe that isn't too cold and rainy and not too highly priced?
It's possible that you'll encounter cold, wet weather pretty much anywhere in Europe if you visit in December. Even Crete, which isn't terribly cold, with average 24-hr temps at almost 60 degrees, gets nearly 4 inches of rain in December. At least it's fairly cheap compared to the major Italian destinations. But when I think Crete, I think outdoors. Best strategy might be to go wherever suits you and to plan mostly indoor activities. A city with a good subway system like Berlin or London lets you get around efficiently without getting too wet, at least.
We have been to London, Scotland and Austria in late Nov/early Dec. Loved all of them! Scotland and Austria were a little bit cold- but not unbearable at all. London and surronds were sometimes a bit rainy (parts of a day here and there- most times we lucked up- even had snow flurries there a couple of years). In fact London was never colder or damper than here in Charlotte. Just plan on more indoor (read churches, museums, shopping) activities due to shorter day light time. I really enjoyed our "winter" trips. Oh- and don't forget the Christmas markets- Vienna, Salzburg, London, Canterburry, Edinburgh, Cardiff, Windsor, York and others have great markets. Of course Germany leads the way there!
To actually answer your question, you best chance is the coastal area of the Med -- Spain, Portugal, Sicily, parts of Italy. Remember most of Europe is further north than Boston. It is going to be cool and not sure how rainy. Portugal would be best for price.
weather of course unpredictable...i was in rome a week before christmas in 06 and it was very mild...this past december i was in florence and it was fairly mild and then a very rare snowstorm hit and shut everything down for days...