I think I made up my mind, help is still appreciated though (please warn me in case I should avoid a selected hotel) :

Sheraton Sukhumit in BKK.

Sheraton Grande Laguna in Phuket. (both for sure)

Westin Sydney or Four Seasons. W seem to be not that good. Great central location of the Westin. Undecided.

Should I try the Sheraton Southgate in Melbourne ?

Is there any recommendable Starwood property in Singapore at all ? Ritz-Carlton looks like my first choice. Four Seasons is good for business though.

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Take care, especially while being abroad.