That's a very adequate budget for good hotels in Phuket. You can sort your options here when you have put in your dates.
Phuket: http://www.cheaperthanhotels.com/Thailand/Phuket/
Patong Beach is one of the nightlife areas , but i wouldn't get hung up on ny particular areas as accessability is no problem : http://www.cheaperthanhotels.com/Thailand/Phuket/Patong-Beach/
If you want to stay close to the nightlife, You'll probably want to stay on Patong Beach. That's the main tourist beach on the island of Phuket. It does have the dirtiest water of all the beaches on the island though.
Here's a link to Thaihotels.com.
http://thaihotels.com/hotels/thailand/phuket/location/3
You can find information and make a booking at practically every hotel on Phuket.
If you want to stay at a nicer beach, go to Kata or Karon. There will be shops and restaurants close by but you'll have to take a tuk-tuk into Patong for the nightlife.
You need to look for somewhere near to Patong Beach. That is where all the nightlife is as well as cheaper hotels.
Please be careful, though, when choosing a hotel. There are some dodgy ones there. Book through a reputable agency - there are plenty on the internet if you look properly. Check them out at tripadvisor.com or a similar website.
Patong beach and Karon beach suit you if you want to enjoy night life, there are lot of hotels for your budget
Try this site to find out hotels
- http://www.thailand-gateway.com/phuket_hotels.html
- http://www.thailandhotelsdestination.com/cheap-phuket-hotels.html
If you go to Patonhog check out some hotels near Sainamyen school. There are about 4-5 hotels priced at 500 thb/nght, thats about a 5 min walk to the beach, there some bars in the area you also walk to Sutoi Bangla about 10 mins away.
Go to le tong or novoel.abt 800 bhats for all of you.maximum 1000 bhats.on patong beach.i mean kalim beach.
You may try for these cheap hotels......
By The Sea Khao Khard Beach Phu
The Royal Phuket Yacht Club
Connect Hotel
All Seasons Naiharn Phuket
Khaolak Sunset Resort
Diamond Cottage
Good luck !
Phuket Hotel, Brothel and Casino
What else are you planning to share between the three of you?