The culture then the beach is a good approach but Europe may not be first choice as the kids have already been to London twice, Paris, andmost of Italy and I've been to Madrid, Zurich and much of Germany and would rather not re-visit at this point. Plus there aren't too many Hyatt resorts around Europe and using Hyatt is a requirement for this trip.
Australia does sound good (and the kids have asked for it) but my wife and I have been there twice and I would like to return there only after we all get diving certified for some barrier reef dives (we only snorkled last time)- so that would have to be a few years away as my 9 year old is too young. Plus I am not sure August is the best time for Australia (we went in May last time and it was perfect).
Please keep the suggestions coming.