Does this hotel provide a shuttle service to Phuket walking street or the weekend markets in Phuket town? If not is it easy to get a taxi from the hotel at reasonable prices?
You can arrange taxis at the front desk this is if you are travelling a little further away from the hotel. But if you walk outside to the main road there are plenty of Tuk Tuks, they generally will take you anywhere close by. But with these guys make sure you negotiate a fixed price prior you leaving as they tend to make an exorbitant cost at your destination should you not have agreed on a price prior. There are also plenty of tours which you can take to show you around the area. These then take you to the Big Budda, the Temple, Karon lookout point, etc. Enjoy
You would need to get a taxi I think. Although we didn't get a bus or taxi. Some tours go to the markets and phuket town.
The Bangla Road "walking street" is only 2 minutes walk away!
As for using taxi's on Phuket there is a "cartel" operating so all taxi drivers will charge you the same, no negotiating and way way more expensive than anywhere else in Thailand, so much so I always hire a car when going to Phuket.
Get an answer from Patong Beach Hotel staff and past guests.