Phuket has 35 beaches and the best online guide to find these is from the excellent Phuket101 website.
Some of the beaches are reachable by bus and most by motorbike. Use the smartphone app Grab taxi if you don't want to drive yourself.
Check if there is any group gathering on the Gay Outdoor Phuket website. Once a week there is a pool party with dinner at Phuket Gay Homestay and there are usually different beach outings arranged by the gay hotels.