Hi, I had visited Jogja last year.
Hotel, just ask and the friendly taxi driver take us to find a cheap hotel along Jalan Maliboro. My hotel was near the supermarket there and some streets shop. Its quite happening at night.
We choose hotel near the supermarket because there is a sign of KFC there.

Since the hotel also got tourist guide, so we hire him for a one day trip. The charge can't remember but cheaper that what the taxi driver charged.
First night, went to watch Ramayana Ballet-about old Java. Lot of foreign tourist.
Day 1 - 1. Went to catch a sunrise at Candi Borobudur..wake up around 4.30 a.m. There are several small candi there but the Borobudur is the biggest.
2. Went to Candi Prambanan - small but beautiful candi. It was affected by previous earthquake, so they put up a fence covering the candi. So nobody can go near the candi.
3. Went to some gold shoppe. Nothing to bought.
4. Went to Keraton-just like Istana Negara in Malaysia.
5. Went to some old ruin palace - a swimming pool for the sultan's concubine. Beware of slippery floor.
Last check out from the hotel and went to Train Station- next journey, Bandung.