All good suggestions up there re routing. I would just note that going through NRT or HKG rather than SIN or BKK would save you some back tracking, but other than a couple of extra hours it is all pretty much the same so just depends on which carrier/alliance you want your miles with.

Within Indonesia, you will have to take a local carrier which is a little dicey. You will be best off flying into and out of Yogyakarta on Garuda which is better than the rest of the bunch. On your way out, if you are going to Singapore you will be best off flying to Jakarta on Garuda rather than back to Bali to avoid backtracking. You can get back onto SQ there and it is a one hour flight up to Sing.

I would recommend spending a day in Yogya as well since you are going all the way to Central Java, and visit Prambanan in addition to Borobudur.

Have a good trip, TJ