Any public hospital (Rumah sakit) can do i safely.
I am not saying that Indonesian hospitals are good, mind you. As it would be too complicated to give medical students a comprehensive teaching, the medical school mostly rehearse the basic gesture again and again. So they definitely can make a vaccine.
I would say the problem will not be cleanness but logistic inefficiency.
They most likely don't have any vaccine in stock(even in a fancy clinic) and will ask you to come back next week. And will ask you to go to 5 different places to fill some forms.
Expect the staff to be extremely surprised. It may take time for them to understand/believe your request. Prevention is extremely unusual in Indonesian culture.
hospital : rumah sakit
Rabies : "Rabies" or "penyakit anjing gila" (mad dog disease)
vaccine : vaksin
Come back latter/tomorow : kembalik nanti/besok