There are many different beaches on the island. The most crowded area is Patong, so i would avoid there is you want quiet. Kata and Karon are still busy, but Kata especially is not as much of a party area, has a nice beach and restaurants.
Quieter again is Kata Noi, this has a nice beach, out of the main tourist route as it is around the headland and not on a busy connecting road.
Naiharn is in the south of the island and has good restaurants and beach, but be aware not all dive operators include transfers from this area. It is not too far from the daytrip pier though easily reachable by a short taxi ride.
There are quieter beaches in the north of the island at Surin and Bang tao, but you will find yourself more isolated and transfers will be extra for trips.
There are many dive companies around the island, who can arrange the diving and snorkeling for you at sites which are suitable for everyone. You dont necessarily need to be next to one at your hotel as you can prebook before you arrive All of the companies have weekly schedules for the boats that are easily found on the websites. Look at trip advisor and get an idea of the company you would like to dive with, look at the number of people on the boats and service offered, then you can book by email.
Try contacting several dive centers and see what response you get. if you would rather meet face to face then you can narrow down the choice this way before you arrive.
Dives that would be suitable are the Racha Islands, Phi Phi, Shark Point, anemone reef Koh doc mai, these can all be dived with an open water license. More advanced dives like the King Cruiser you should have advanced and some experience.
