Originally Posted by
Enkidoh
Apart from the arachne gear for melee classes having a basic body tattoo on the upper arms and shoulders included (worn by NPCs at the ROG Guild), the closest to body tattoos in the game is the 'Legacy Mark' (also known as 'the Mark of the Twelve') that identifies a player character as having originated in the original version of FFXIV (1.0).
This appears on the upper back and can be turned on and off at will by typing /lmark (I keep Enki's one kept on by default, even if it's usually hidden by armour or clothing). However it is only available for characters that were created in FFXIV 1.0 and then transferred into FFXIV ARR - new characters do not have this mark I'm afraid.
Hence maybe body art could be offered by the aesthetician as an option instead? :)