Prambanan

Long treated like a poor second sibling to Borobudur (it used to be cheaper to visit, but not any more), Prambanan is super easy to reach from Yogya.

You can take one of the Prambanan Ekspres - aka Prameks - trains (for details of these, see my Solo post) or bus 1A which runs down Malioboro, along the north end of the Kraton, and then heads east, past the airport to Prambanan.

Popular with local tourists, and students looking to practice their English

The temple complex consists of the main grouping (surrounded by piles of stone that were once hundreds of smaller temples), plus 3 other temple complexes within the greater park area.

The reconstructed temples (and what a jigsaw that must have been) are filled with reliefs of animals and plants, and most of them allow you to go inside.

For some reason, this reminds me of my brother and me as kids....

The other temple complexes (Candi Lumbung, Candi Bubrah and Sewu temple) are all considerably quieter than the main complex, and you can easily find a quiet corner to take a break. 

One of Sewu's big boys

Pack a sunhat or umbrella / parasol, as the site offers little shade - I believe you can rent parasols there - I certainly saw plenty of abandoned ones around the complexes.

If coming by bus 1A, the bus drops you off at a small depot on the other side of the main Solo-Yogya highway.

Cross the road at the lights, and walk in the direction of Solo. You'll pass 3 gates. The first is locked. The second is a staff entrance. The third is the pedestrian and motorbike entrance to the parking lot. Go in here (the 4th gate is around the corner, where cars can go in) and cross the parking lot, angling a bit left, to see the entrance pavillion and ticket offices. The foreigner ticket office is on the far left of the pavillion, and has the last clean, Western-style toilet you'll see (I suggest you use it). Once you've paid your extortionate fee (350,000 IDR; you can buy combined tickets for Prambanan and Borobudur that save you a little money, but they're only good for 2 consecutive days, so you can't spread out your visits out avoid getting over-templed), and been given your photo-bearing entrance ticket, head out back to the welcome area to claim your included cup of tea or coffee (well worth paying 10x the local price!).

I have no idea what they spend all the vast amounts of money from ticket sales on.... it certainly isn't on cleaning the public bathrooms away from the tourist entrance....

Yes, the temples are ludicrously overpriced, but they're also incredibly impressive. So clench your teeth, pay the money, and go.