Unless it's something really unusual or specialised, I would probably just take my chances in Jakarta. In most cases the medicine, diagnosis and treatment is fairly clear and you can just check they are not making any mistakes. If I did go abroad for treatment (as I have done once) I would probably choose Penang, Bangkok or somewhere in continental Europe ahead of Singapore.
For the standard stuff I go to a local clinic which has an expat GP. I'd imagine if I had something serious that requires brain/open heart surgery (knock on wood) or something I'd probably go out of Indonesia though.
In saying that it's not all bad in Jakarta; our OBGYN obtained his degree from and worked in the UK for over 20 years before moving back and is fantastic. I also know quite a few dentists and dermatologists that either obtained their degrees or did advanced education/work abroad.