The Temple of Borobudur is one of the biggest Buddhist sites in south east asia and is located outside of Yogyakarta (Java, Indonesia). It is definitely worth to visit. Most people get there early to watch the sunrise which means it will be packed. What you can do is you just go for sunset and avoid the masses of tourists.

We went there by scooter. It is a fairly long ride to the temples but that gives you the flexibility of choosing the time when you want to go. (Borobodur - sunset, Prambanan - sunrise)

Candi Prambanan is the largest Hindu temple site in Indonesia. The temple is dedicated to the Trimurti (Brahma, Vishnu, Shiva). You can actually walk inside and search for the gods. If you want to be (almost) by yourself, you should go by sunrise as most guided tours go to Prambanan at sunset (check opening hours). There are also some temples nearby where you can watch the sunrise and right after go and visit Candi Prambanan. Here are some pics of what you can expect.

Sometimes you will find schoolkids who want to show you around the temple. You do not have to be suspicious. They just want to learn english. If you are keen on learning more about their culture, you should walk with them for a while and ask as many questions.