How you split your time depends heavily on how long you have — here are three starting frameworks to adjust from.
3 days: hit the highlights
Base in Patong or Karon. Day 1: settle in, beach time. Day 2: a Phi Phi Islands or James Bond Island day tour. Day 3: Old Phuket Town in the morning, a viewpoint at sunset.
5 days: add a second base
Split your stay — 3 nights on the busier west coast (Patong or Karon/Kata), then 2 nights somewhere quieter like Nai Harn or Kamala. Fit in one island day trip and one cultural day covering Old Town and Wat Chalong.
7 days: go deeper
Everything above, plus room for a second day trip (Similan Islands, if the season allows, or the closer Racha Islands), a proper food-focused day in Old Town, and enough slack to skip a day entirely if the weather turns.
Whatever the length, build any weather-dependent island tour into the earlier half of your trip — it's much easier to reschedule around a rained-out day if you've still got days left.