Exploring this area is fun and easy if you have your own transport. Local bemo buses do run the length of the coastal road, but you will not have the flexibility to explore as you might like.
The Amed area and the SE coast in general is arid, with corn and cattle replacing rice production. Along most of the coastline curving bays are lined with painted local fishing boats, moored on the beach for the next night’s work. The fishermen in this area tend to gather in the daytime under a shady tree, sharing grilled fish, chilis and arak, the local palm wine. They are often very glad to welcome a foreigner to join them and if you have an hour to spare it can be quite entertaining. Do not let your lack of Bahasa Indonesia be a barrier, these guys won’t care.
The SE section of Bali has one very important temple, Pura Lempuyang Luhur, which is one of Bali’s kahyangan jagat (directional temples) and protects Bali from the SE. Pura Lempuyang Luhur can be visited easily and is not a tourist trap. Accessing the temple from Amed means a 10km drive west to Abang, then follow the sign for the temple in the direction of Ngis Tista. You will come to the bottom of a staircase you will see 2 nagas guarding the entrance (sounding like Lord of the Rings?). The long staircase with 1700 steps, could take 2 hours to climb. The best things about visiting Pura Lempuyang Luhur is the view. Gunung Agung can be seen perfectly through the split gate temple entrance and for people with extra energy, a 90 minute hike will take you to the summit of Gunung Lempuyang with fine coastal views. Be sure to bring plenty of water, even as much as 5 liters a person, because its is hot and dry out there.
Incidentally when you come back from your exhausting hike you might head to Tirtaganga for a freshing dip in the freshwater Royal swimming pools. Tirtaganga is only 4km from Abang. Food and drink are available at Tirtaganga as well as accommodation.
Another adventure that hikers could try is the route to the 5 Holy Springs. According to legend there are 5 springs on the eastern slope of Gunung Seraya that all taste different. Called Toye Masem, the springs are accessed by driving 2km south of Amed to the village of Bunutan. There is a road running inland from there just over 4km to a small village named Bangle. The first spring is about 1km west (uphill) from Bangle. You will pass through rugged scenery with casava, chilis, corn, soybean and some bananas being grown. Each spring has a bamboo pipe to enable drinking and has a shrine to protect it. Views are good from this location looking east towards Lombok.