Bang Pae Waterfall is located in Khao Phra Thaeo National Park, Thalang, just a bit north of Phuket Town. It's a popular location for people who live in Phuket to visit once in a while, to take a swim in the waterfall and have a picnic, the trees cater for the needed shade from the hot sun to make this an ideal spot. The waterfall itself is more active in the wet season, and even if it's one of Phukets larger falls, it's still quite small compared to what can be found around the globe.
Even if the waterfall is most active during the low season, when there is more rain coming down. It's still enjoyable during December to May, and you will be able to dip into one of the pools, or take a shower from the main drop. Just be aware that it's quite slippery around the fall, and make sure to protect yourself, not to mention it's in the jungle, where mosquitoes are quite common.
The Gibbon Rehabilitation center is also located just on the way to the waterfall, you can here the sound of gibbons it as you are getting closer, not to worry, they are kept in cages, and you wont be allowed to go close. There is a few restaurants and food stalls here, just in case you did not bring your own lunch. And do remember to clean up after yourself, and remember that food and drinks are no allowed around the waterfall.
Now days there is an entrance fee to the National Park for foreigners, 200 bath per person. But do keep the Ticket, as it is valid for visiting other National Parks the whole day. There is also a small parking fee for motorbikes and cars 20 - 30 bath. The trail up to the fall can be quite demanding physically, even if it's been improved with some concrete reinforcements, there is still plenty of trees to keep out for.
Another of Phuket's famous waterfalls is located on the other side of the hill, Ton Sai Waterfall, you should plan to see them both in one trip, as it's only a 20 minute drive around from Bang Pae Waterfall.