Just one overnight? Where is your liveaboard departing from (or which boat will you be on and I can look it up)? If you are flying in and all you want to do is rest overnight and relax on a beach to get past some jetlag before diving, AND your LOB is departing from Khao Lak/Taplamu, you might want to stay right up near the airport to save the transit time down to the southern beaches and back north again.
OTOH, if your LOB is departing from Phuket, and specifically from Chalong harbor, you can stay at any of the southern beach towns: Patong, Kata, Karon. From Patong to Chalong is a good 30-minute ride after the mini-van picks you up; Both Kata and Karon are about a 15 minute ride to the pier and there are tons of cheap beds in these two towns. Alternatively you could stay at Chalong itself--many of the people around in the evening are dive pros as many of us live in the area, and it's not a big tourist area except for daytrippers using the pier. If your boat is one of the few that departs from Patong Bay, well, it's all about nightlife in Patong, so if you want to party all night before diving stay somewhere near Bangla Road or Soi Sansabai. If you want to relax, stay elsewhere, such as up on Nanai Road.