On crossing the Friendship bridge you'll find the islands highways to be in excellent condition for the most part. The eastern region tends to be flatter and is plains. The center-western fringe is mountainous (theyand ticky to navigate across unless you take care and don't rush things.
Areas to travel to are legion, the waterfalls lie off to the east out of Patong Beach.
East of Kata on the main road is the firing range and elephant camp for tours etc. Further east will take you into the plains and on to Phuket Town and Pier.
Provincial Map of Phuket