Originally Posted by
MSPeconomist
Budget makes a difference. I was going to suggest Singapore, Hong Kong or the Westin Tokyo because these are cities where I could easily be happy for a month. Another idea is Kuala Lumpur, which had a number of Starwoods and is generally an inexpensive city.
Do you want a resort-type property? Any visa restrictions? Something like LRM Shanghai (which has a good lounge) would be in the budget if you can find good rates for most nights.
The OP really seems to be wanting a property that is non-city, so most of the options you listed probably won't work for him.
South-East Asia is where I think OP's most options will land, except for the "not too hot" part.
I would have a look at the Le Meridien Koh Samui, it can be had in the $200 range and checks off many of your boxes. Sheraton Krabi, Le Meridien Phuket, etc... The properties are not so far apart that you couldn't spent a few weeks at one and a few at another.
Other potential places to look are Bali and Langkawi, but both of those locations could be even warmer.
For pool, beach, hiking, etc...:
Le Meridien Phuket:
Le Meridien Koh Samui: