If you don't want to meet many people and prefer to explore the quieter monasteries, try to walk around. There are nearly 80 other quiet and nice monasteries to explore in the forests.
法雨寺, 法雨禅寺
At the foot of Fodingshan (Foding mountain), at the north end of 1000 Step Beach.
慧济寺, 慧济禅寺
The lazy can reach the temple by cable car (¥40 return). Take Bus 2 from the port (¥10). More active visitors and pilgrims take the concrete steps from near Fayu Temple. It takes about 1 hour to climb the mountain. If your interest is old military installations, turn right soon after the start of this stair ascent up a smaller set of stone steps. After 10-15 minutes, this continues through a series of anti-ship and anti-aircraft gun emplacements with gunner accommodation and ammunition stowage built into the cliffs. Everything is in very good condition, there is no impediment to access, and looks like the PLA continues to take an interest. Also being off the beaten path, there is a complete absence of other visitors. You can then continue to the summit of Fodingshan on earthen paths, using common sense navigation because nothing is signposted in this area. But this is less interesting.
普济寺, 普济禅寺
This is the most accessible and famous monastery on Putuoshan. Nearby there are hotels, restaurants and interesting shops. A public ritual performed by the monks runs from 4:30AM to 7AM. It is crowded at this time, so unless you are interested in the ceremony, it's best to visit the temple outside these hours.