There are jump puzzles in the Gold Saucer, Kugane, Shirogane (no reward) and a couple other locations.

Real puzzles? There is one in the MSQ in Rak'tika in I think 5.2 or something. There's also the Faux Hollows little board for which you have to do an extreme trial first.

Basically every difficult combat encounter boils down to some sort of puzzle.

There is a really cool riddle questline in ARR, very difficult. The Variant Dungeons also have riddles in them that are quite difficult to solve on your own.

Beyond that uuuhhhhh.