Follow-up:
The first thing I bought once I got our from the airport was a SIM card. Our driver stopped at small shop where I got SimPATI for 115K IDR which included 1.1GB 3G/internet traffic.
That card/plan was only for internet because I did not need voice calls, it was an excellent value and I am not sure if I used more than 30% of it. Coverage was good - 3G+ in Ubud area and mostly 3G in other areas.
It was quite useful to have the card. What was frustrating - no idea how to check the usage of the traffic because instructions were only on Indonesian. Either way, I do not think that I've used more than 30% of the allocated limit.