Kaliurang is in Central Java.
Kaliurang, when Mount Merapi is not erupting and making this town a prohibited zone, is the equivalent of a Hill station or Hills retreat where in colonial times, wealthy residents of Yogyakarta or Surakarta would have holiday or weekend homes here. Also the local rulers would have had their residences in the cooler air on the southern side of the volcano.
In the 1960s and 1970s, when southern eruptions were not a regular occurrence at all, a number of the places to stay developed legendary status. Vogels was the place to stay, and regular updates of Bill Moon's Indonesia Handbook would have details of the southern approach to the night walks to the peak of the Volcano.
The 1990s and 2000s south flowing eruptions and gasses have tended to make a significant dent in the liveability and general access to Kaliurang.
It is advisable to investigate the condition of the volcano, and general accessibility of the town.
When the eruptions were not spewing southwards, it was also the location of one of the 4 or 5 observation posts of the Volcanological survey. The post is named after the hill, Plawangan - and when there is clear air, and no euptive gases heading south, a very good view of the southern slopes of the volano are possible from the Plawangan hill. Another hill just west of Plawangan is Turgo, where a mysticall and significant Islamic saint is buried.
The largest nearby city is Yogyakarta located 25 km (16 miles) south. Starting in Yogyakarta, Jalan Kaliurang is the road that goes all the way to this location.
There is a fee entrance (3000 per person on weekends) to access the Kaliurang village.
Walking in the cool air of the higher ground is the best way to experience the place.
Tlogo Nirmolo and Tlogo Muncar are two forest areas located at the south base of Mount Merapi, north of the Kaliurang village. There are some interesting and not too tough treckins you can do there. Ticket access allows visit of both parks during 1 day (you may need 3-4 hours to visit everything).
Ticket for locals or students (including foreigners that study in Indonesia or with kitas): 5000rp. Ticket for foreigners: 150.000rp
Indications along the trails are quite good and you can't get lost, also you can use the offline maps like OsmAnd or Mapy.cz for better guide yourself in the treckings.
This forest includes the visit of many Japanese caves (Goa Jepang) constructed during the second world war to be used by the Japanese army to protect from the allies attacks. There are a dozen of those not profound (10m max) caves and there is a man that can rent you some lightorch (although using your phone's torch would is enough). It takes 30min trecking to the caves from the entrance.
Also a much steep treck to the summit of the Plawangan hill is available (ask the entrance gard if the visibility is good). (40min).
This park is more visited by families and Indonesian couples since it includes a quite magnificent waterfall called Muncar (id: Air Terjun Muncar), after raining the waterfall is more interesting since it can bring lots of water. Also there is a 25min trecking to the top of the Pronojiwo hill with great views towards Merapi.
There is a market (id: pasar) in front of the parking where you can buy tempe cooked in a unique way called Jada tempeh just for 1000rp each.
Also on the road to Kaliurang, at the Pakem village, there is a banana market (5 or 6 stands on the right side) where you can find the cheapest bananas and avocados.
There are many small hotels and villas for rent.