Effie,
A certain amount of misinformation here.
A sixty day tourist visa CAN BE EXTENDED INSIDE INDONESIA, JUST LIKE A 60 DAY TOURIST OR SOCIAL VISA. It has the same code as the other two - B211. The only difference is that you do not need a sponsor to get it...
In theory, just like a social visa, you can extend it four times, 30 days at a time, up to six months.
Though you don't need a sponsor to get it in the first place, you DO need a sponsor to extend it, but this can be anyone; they only need to fill in a form and provide a photocopy of their ID card. And here's the good thing - unlike a social visa which is tied to its original sponsor for its entire validity, you can have different sponsors, in different places, for each extension of a tourist visa....
In Bali, reliable agents like Bali Ide will charge Rp650,000 for an extension of a 60-day tourist visa (though you will have to find the sponsor yourself); it apparently takes about ten days to process (for an insight into haw much money is being made and how much time is being wasted, in Surabaya it costs Rp265,000 to extend the 60 day tourist visa if you do it yourself, and takes three or four days).
From reports of people who have extended a tourist visa beyond three months, things get trickier on the second and third extensions, and I've not heard of anyone extending it up to the full six months, but the first extension IS very EASY...
At worst, for a six month stay in Bali, you could certainly manage it on 60-DAY TOURIST VISAS with just ONE visa run to Singapore (you can get a 60-day tourist visa there yourself in three days, or using the service of an agent - Hanna Express is good in my experience - get one in one day. The only thing they do want to see to support the application is a ticket out of Indonesia. This can simply be the cheapest Air Asia flight to Singapore, and they seem not to be concerned about it being dated beyond the initial validity of the visa).
ALL OF THIS INFORMATION IS ABSOLUTELY, CATEGORICALLY CORRECT AND BASED ON FIRST-HAND EXPERIENCE. Anyone who tells you that you "cannot extend a sixty day tourist visa" is misinformed. It WAS the case that until several years ago the 60-day visa issued to tourists had a different code to the social visa, and couldn't be extended, but about three years back they changed it, made it a B211 too, and since then it has been extendable - and lots of people HAVE extended it...
A very new change has now, supposedly made the 30-day visa on arrival extendable, but - I think - only once. This is certainly an improvement, but probably of limited use for someone planning a six-month stay.
I would go for the 60-day tourist visa.