We are pretty no frills travlers and took the public bus, trans jogi. It's 3500 for a ticket to anywhere including transfer as long as you don't leave station. Actually easy and straight forward. Download the moovit app for an excellent bus route information, truley a must have and fantastic app.

That being said the hotel offers a free shuttle to Malioboro street on the weekends with 3 pick up and drop off times. I did not use but am sure it's great. You could also have the hotel call you a taxi, wich we did to the airport, and it worked flawlessly. It cost us 50k to get to the airport at 5am, so price may vary with more traffic. You could also download the blue bird taxi app if you have a local number. We used it on the island of Lombok and worked GREAT!

You are correct, hotel is a bit out of the way, but found it a good area for our tastes. The large new mall has lots of options for food as well as a grocery store. A side note, we visited Plaza Ambarrukmo one day, another mall, and walked back to the hotel, a bit of a walk, but....JL Nologaten street just west and north of the Plaza was great! A locals Malioboro st if you will, wich I wish we could have visited longer. You should check it out. We were walking the street just before sunset and looked to be just getting going.

Also if you are looking for a great expirience, contact studio 76. Wife and I went to make silver jewelry in kotegede. Agus is the owner, a great guy! Made two rings at the 2hour course LOTS of fun and very unique, only 200k each. He is a photographer at heart but has a silver studio as well. Check gogle maps for info.

cheers!