I've visited Candi (temple) Mendut and Borobudur twice in a few days. The second trip was much better than the first, and also allowed me to see Prambanan.
The first time was for the 2550th Waisak ceremony, which commemorates (Gautama) Buddha's birth, enlightenment, and death. Activities take place over a period of nearly two weeks, but the major public participation occurs at the full moon, with a ceremony at Candi Mendut (there's a monastery there), a ~4km procession to Borobudur via the small Candi Pawan, and then a longish ceremony once Borobudur is reached.
It was the most important day of the year for an Indonesian-speaking Buddhist. Unfortunately for me the day was both rushed and underwhelming - I think I would have been better braving the pickpockets on the public bus but going at my own pace. I was in a tour group and the guide didn't really explain very much. We spent about ten minutes at the crowded Candi Mendut watching the monks before skipping Candi Pawan and walking to a vantage point to watch (and join) the procession that passed about an hour later. After a slow hot walk we arrived at Borobudur to see the monks distantly circumambulating the stupas on the temple's upper levels. Once they descended, they sat on stage and chanting and lectures (in Bahasa Indonesia) took place. Due to the occasion, Borobudur could not be ascended. We left the temple grounds before nightfall.
The highlight of the day was seeing Gunung Merapi for the first time. The three temples are on a straight line with the volcano and from Borobudur it could be seen clearly (there were some clouds round its midriff but none obscuring its peak). You can also see it from a couple of bridges near where I'm staying in Yogyakarta but I didn't know that at the time.
For the second trip we left at 5am from Yogya in order to reach Borobudur by sunrise (we didn't). I'm still not a morning person but it was worth it. Borobudur is a ten-tiered temple; the lower seven tiers have reliefs detailing (Guatama) Buddha's life and other Buddhist imagery; the upper three have bell-like stupas containing Buddha statues around a large central stupa. The levels represent progress towards Nirvana and perfection - the central stupa is unbroken while the other stupas have holes through which the statues inside can be seen. There was one statue which is supposed to bring good luck if you touch its fingers (if male) or foot (if female) - it is the only one with its hands in the Wheel of Dharma posture. I didn't - there were some Buddhists protesting against the activity during Waisak, plus I don't believe in luck =). While we rested at the top, trios of namebadged Indonesian English students practised their conversational skills on us. My trio talked sports (Football/soccer is very popular here) - and were rather fluent for only having six months' study.
Departing Borobudur we saw Pawan, a small temple with nothing inside, and stopped at Candi Mendut to see the Buddha statue inside - the largest in Indonesia. Like the tiers of Borobudur, the interior of Mendut was inaccessible during Waisak.
Throughout the day the minibus stopped to allow us to look at Merapi - a few of my fellow travellers were in volcano chaser mode and had been out to look more closely at it the night before. It was belching quite a lot of gas/smoke but there was no major activity - no jets of lava or anything.
Prambanan is a complex of 50ish Hindu temples/shrines, but we only had time to see those in the main complex. Originally there were many more, but most of the small shrines were raided for their stone (I saw some that has been used for paving in Yogyakarta's kraton) and are now just piles of rubble - only two of the original 224 small shrines have been restored. Basically, everything collapsed a millennium back in a major earthquake and it's only in the last few decades that the temples have been restored. The three major temples there are dedicated to Shiva, Brahma and Vishnu and have reliefs depicting the Ramayana and the life of Krishna decorating the inside their outer walls. Where Borobudur is pyramidal, the temples of Prambanan are more vertically stacked, giving me the impression of beehives.
We returned to Yogya in the mid-afternoon, by which time Merapi was concealed.