Welcome to the forum. An intro would be nice sometime.
THIS LINK gives some of the hotels recommended by forum members.
KN Guesthouse fits your criteria, inroom safe, A/C, TV, Pool, close to Bangla Rd nightlife.
KN Guest House, perfect comfort and location, Phuket Island
Nice beaches from Patong include Nai Harn (40mins by tuk tuk)
Kata and Kata Noi 25 mins away
Karon 20 mins
Kamala 20mins
Laem Sing 25mins
Surin 25 mins