Eric,
As Herb mentioned, there seems to be little good shore diving in Phuket. "Dive Guide Thailand" by Paul Lees seems to list only three shore dives in Phuket. All are rated one-star (poor) on a five-star scale. They seem to be used mostly for OW training.
If you want to try a day-trip to the Similans from Phuket, Marina Divers offer one-day two-tank dives to various sites in the Similans for US$101 via their own fast catamaran. Just be forewarned that if the seas are the least bit rough, the trip will likely be diverted to a closer, alternate dive site. At least that was my experience last Chinese New Year.
They (along with many others) also offer slow boat trips to closer dive sites, where you can squeeze in three dives per day for roughly US$50 per trip. Anemone Reef and Shark Point (Hin Musang) are not to be missed IMHO.
I hope this is in some way useful.
Cheers,
Michael.