Each continent is a tall order, but I can give you a couple from personal experience.
In Europe, I was very impressed with Mar Bella beach in Barcelona. Urban beach with good facilities and good usage of the clothing optional section. Noting that this question was asked under LGBT, let me add that Mar Bella has a mix of straight and gay users. All seem to get along just fine.
In the Caribbean, Orient Beach on Saint-Martin has a good mix of devleoped and undeveloped beach zones so that anyone can find a place they like.
Despite what some believe, the US actually has a number of places. On the east coast you have Sandy Hook, New Jersey in the north and Haulover Beach in Florida to the south. On the west coast you have a number of options in California and even a couple off of the Columbia River in Oregon.
With a little searching, you should find good options around the world, except possibly for the Middle East.