You are asking the wrong question.
Finding uninhabiteds island is not a problem, there are countless ones in Oceania or the Caribbean.
Marooning was the term of leaving someone on an uninhabited island and it was considered a capital punishment.
The reason is simple: What do you want to do there what you cannot do with a big yacht or a house on a inhabitated island ? You have already the precondition that you have enough money. With a big yacht you can travel everywhere, replenish stocks and do what you please. A house on an inhabited island gives you social life to enjoy.
Living on an island grows stale very quickly. Most uninhabited islands are for a reason uninhabited: They cannot sustain life for one or several persons, so replenishment of stocks and therefore contact with the outer world are a necessity. If you cannot avoid contact why living on an island (instead on a yacht or house of an inhabited island) in the first place ?
What about friends ? They may find it cool to party some time, but sooner or later a
problem occurs: Cabin fever. Every time a group is isolated and have no possibility to withdraw, it causes irritation and finally aggression.
Anyway, all islands are under a jurisdiction. While officials may never find out what you are doing, once they know they can forcibly evict and punish you. And the law also applies for everything you have done, so no room for misbehavior. User cpast provided in the comments an example:The attempt to elevate the unoccupied Minerva Reefs near Tonga to an own nation. Tonga forced the claimants to abandon their attempt.
Forget the idea.