Merapi National Park is located in Kaliurang, Yogyakarta. It can be reach from Zest Hotel Yogyakarta by driving via Jalan Yogya-Turi for about 60 minutes, depends on current traffic.
Have your gut tested to try off-road ride on a Willy's Jeep, exploring the area around the line of cold lava or hot volcanic ash flow produced by Mount Merapi during eruptions. The steep contour of the land forces the Willy's engine to work hard to run through the sands and the scattering big rocks. The car will rock heavily, you'd need to hold on tight and align your body movement to the jeep so you wouldn't throw yourself out of the car. It may scare you a bit, but will surely attract you like opium that you just can't get enough of. Apart from the fun and adrenalin rush.
For Jeep rent: IDR 450,000 - Idr 600,000 and you will be guided by professional off-road driver