Reviving this thread. Maybe some have changed their choices/opinions now (travelled more? experienced a city again and changed your mind?)
NYC
No explanation needed. If you are rich, there is no place like New York City in the world to live in. It has more to offer than anywhere else; food, nightlife, women, 4 seasons, etc etc etc, you can go on for days
Paris
Just like NYC but this would be my base in Europe. For a rich man to base himself in Europe, he would most likely be choosing between the 2 best cities there, Paris or London. And for me, London just doesn't do anything for me. Paris on the other hand is glorious in all aspects just like NYC.
Los Angeles / Miami
If you are rich, you need to have a place in one of these 2 no matter what! Beautiful weather, sexy women (probably the best in the country), a lot to offer... and you would not have to worry about safety because you would be living in an area like Beverly Hills/Miami Beach/Palm Beach/Coconut Grove. This is a tough choice between the two though... LA has the year round warm weather, the beautiful scenery of mountains and forests all around you, and in general just a solid city to live in. Miami on the other hand has the turquoise crystal clear water, warm beaches, sexy latinas, strong sun and tropical lifestyle. Can't choose between the two at the moment
Rio de Janeiro / Florianopolos / Honolulu
Gotta have a winter estate! Brazil is a must for the women, the scenery, the weather and the beaches; again tough choice between 2 great cities for different reasons. I also threw in Honolulu to make it even harder to choose, but having a place in Hawaii would be amazing. Don't know if it would be amazing enough to say no to a place in Brazil though.
Hvar
This would be my base for Eastern Europe. It is packed with girls from all over europe, especially eastern europe, during the summer. This place is getting more popular every year, celebrities are even beginning to head over there for vacation. It is stunning. The beaches, the weather, the water, the scenery, and the eastern european women. Can't go wrong!
Toronto
Gotta rep my city!