Depends when in Dec you'll be there, if earlier in Dec' you can probably move around OK without pre-booking accomm' but around Xmas it'll be difficult as X-mas/NYE people tend to book in and stay put, then you get a large movement of people around Jan 2,3,4. But at any of these tourist meccas it can be tough finding accomm from late Dec to early Jan.
Phuket's OK, you'll enjoy Patong too if you're a party person and enjoy a few beers. If you're not a party person and don't drink then give it a miss as it'll get on your nerves.
There are lots of organized tours available from Phuket, you'll walk past a zillion tour and travel agents with photos in their shop windows. You can go to PP Islands, PhangNga Bay (James Bond Is), elephant treks, jungle tours, temple tours. Organized tours and daytrips are OK, make it easy to go see places, others prefer to do it themselves, use the LP guidebook and go to less touristy spots. Whatever's best for you works..