Karon Beach is on the west side of Phuket. Go down to the Lotus on the north side of Phuket Town and head west at the major intersection. Plenty of signs. Lots of stuff to do there, but only a 400 baht tuk-tuk ride to Patong. I just stayed in Phuket Town and "commuted" to Patong on the weekends.
I had a condo, and didn't have the scratch to stay at any resorts. A lot depends on your wallet.
Sorry I am not checking in so regularly now that I am out in the bush, else I'd be glad to help you out more.
I'm about 12 minutes south of the Thai border at Koh Kong, Cambodia, now. MUCH less expensive, but a lot less fun than Phuket!
Chook di kruup!