Whenever we arrive in a new country we purchase a local SIM card for our phones. Upon arrival in Tual, Indonesia we bought a SIM card from Telkomsel, the largest mobile carrier in Indonesia with great coverage all over the country. For about 1,500,000 rupiah (about US$10) we got a SIM card and 8GB of data usage for 30 days. Note, this does not include any credit for phone calls or SMS messages. What you do is put some money on credit (I put 100,000 rupiah) and when you make a call or send a SMS, it deducts a small amount from your credit. Once your data is used up, you can purchase more from any kiosk in any town in Indonesia. So, you have lots of data for very little money.
While the price is cheap for internet, the questions are (1) how accessible is a good signal and (2) how fast is the connection?
We have almost always had some kind of connection wherever we are although occasionally we are anchored behind a hill that blocks or reduced the signal strength. If we have a good signal, we almost always have LTE (yes, that's 4G!) and at least a good 3G signal. We do get an 'Edge' signal (2G) occasionally also but still have access to (very slow...) email.
So, I would say that we have had quite good connections almost everywhere we've been in Indonesia and I assume it will continue to improve over time so, bring those iPhones and plan to use them for a tethered connection to stay in touch with friends and get news and weather information.
Hope you enjoy Indonesia like we have!