Sept./Oct. is THE worst time of year for rain in SE Asia, though our summer months are also monsoonal in other parts of the region. I went to Taroko in summer and it was rainy, though thankfully not of the all-day type.

Saw Naadam in Ulaan Baatar last year and it was very memorable. People dress in their colorful best, and the opening ceremony is an amazing riot of colors in motion. Though with the smaller Naadams in other towns you get much closer to the action and the people, or so I'm told. Mongolia would be a great country to travel further afield in (I got to UB and Terelj), but the distances can be great and transit slow. Lake Khusvogol, the far west and the Gobi were the most popular excursions, but you needed at least 7-8 days. Weather in July was delightful (highs 70s, lows 40s, sunny).

I found Vietnam to also be especially rich in both people and scenery photos, though I'd rate the north better for that than the south. Beware pickpockets, though.