If you have extra day in Yogyakarta, you can head over to Borobudur Temple. The temple also part of UNESCO World Heritage Site. The main attraction would be the sunrise from the temple ground overlooking the Mount Merapi. You need to wake up early and go through the private entrance from Manohara Hotel because the main general entrance won’t open until 6AM which is after the sun rises.
Make sure to explore the ground after the sunrise. To see the relief and also many feature of Borobudur Temple.
Another great place to capture Borobudur Sunrise would be from distance (Punthuk Setumbu Hill). Here you can see the vast landscape of Borobudur Temple between the trees and thick fog while The Grandeur Mount Merapi besides it. This can show you the contrast size of the volcano and Borobudur.