Phuket Holidays

My husband and I are planning a holiday/honeymoon to Phuket.
My sister recommends Kata or Karon beaches rather than patong, as she has been there.
We would like to relax etc but my husband is quite adventurous and so we would also like to be able to explore and do some outdoor activities etc.
Is it going to be expensive or annoying to travel from Karon to Patong if we want to go shopping, eating, maybe experience the bars and nightlife?

Any recommendations people have would be appreciated.

We’re 3 students, looking to pay max €30 a night each, preferably only around €20 a night each…. We’re looking for somewhere close to the beach, and also with good nightlife. We’re arriving in early August… Any suggestions? We’re Irish.
We’re planning on sharing a room between the 3 of us by the way!