This seems to all come down to what type of lifestyle do you want in retirement?
Personally, I would like a lifestyle as comfortable as pre retirement - otherwise, what is the point? By comfortable, I do not mean it has to be as expensive or costly, but I don't want to be living an uncomfortable life.
A few points to remember, to live in most S E Asian countries as a foreigner you need either to have a job or have a "retirement" visa which requires proof of funds. Alternatively, you can do the constant 30 day or 60 day tourist visa - but that involves inconvenience and the cost of flying in and out of the country every 30 or 60 days. Also, if you don't have a residence visa, you usually cannot get a long term lease which means you are stuck with more expensive monthly rentals.
On housing, yes, you could find a studio apartment (called a kost in Indonesian) in Jakarta for about US$250 per month. I could live in it for a month or 2 but it would not be somewhere I would want to retire to.
Forget riding a bike or walking most places (unless you have a death wish). The flip side is there are lots of taxis and they are cheap.
You could find somewhere to live in an outer suburb or in a regional city - you would probably be one of the few foreigners and everyone would be looking at you 24 hours a day. It would be fun for a while but I think it would wear thin after a few months.
I am actually a strong advocate of retiring to S E Asia - there are many, many advantages. My argument is, however, don't expect to be able to do it on US$100k. I think if you tried it on anything less than US$1.5m you may come up short (unless you are planning on working rather than retiring).