I think a lot of readers of this thread were thinking 3 days in Manila is probably 3 days too long.

With Jakarta, you were sort of heading in a better direction. I though Jakarta itself was fine for about 2 days but not longer. I would suggest Indonesia with 2 options:

1) Bali, but stay in Ubud not at the beach. Bali is a much better cultural destination than a beach one, contrary to popular belief. Three days is not long though.

2) Yogyakarta in Central Java--Borobudur and Prambanan, sights around the town itself, Mt. Merapi volcano, misc villages. Maybe a better match than Bali for a trip of only 3 days. There are nonstop flights to/from Singapore on certain days of the week, other days you might have to connect via Jakarta.

Non-Indonesia options, if you haven't already been:
--Fly to Kuching or Kota Kinabalu in East Malaysia (nonstop flights from Singapore) and spend a very full 3 days in either of those areas + surrounding "field trips".
--Fly to Siem Reap Cambodia for some Angkor temples and surrounding area. Not a bad 3 day trip. I think Silk Air does this route.

Do you pick places to go based on the hotels you can stay at? I'm not trying to be snarky, after re-reading your post, it occurred to me that your priority isn't really "off the beaten path" (your words) but rather is for quick city trips in 5-star comfort. Which is a valid approach, but the suggestions you'll get might be different.