In SE Asia, the best time is during the winter, after the rainy season, say in late October or so, and before the summer season(March-early June). It is generally dry, sunny and relatively cool then. Same advice for South Asia and Hong Kong/Taiwan, but not for NE Asia (e.g. Japan, Korea, NE China - Beijing, etc... too cold then; Sept-Nov better).

If you know someone in any of the areas that you are considering, or can find a friend of a friend or business acquaintance that lives out here, consider visiting them, and having a 'local' show you around. IMHO that is infinitely better than dealing with paid guides, or going it alone, at least for your first trip.