Currently, with New Game Plus you can replay the following:
  • MSQ
  • Raid series
  • Trial series (Warring Triad, The Four Lords, and The Sorrow of Werlyt)
  • Variant dungeons
  • Hildibrand and Scholasticate storylines
  • Tales of the Dragonsong War (/hknight), Tales from the Shadows (closure for F'lhaminn), Tales of Newfound Adventure (Four Fiends backstory) sidequests, Void sidequests, Louisoix's Legacy, and Tataru's Grand Endeavor sidequests
  • Class, job, and role quests

This is leaving out quite a lot of story content that many of us might want to revisit without having to spin up a whole new character, such as:
  • Tribal quests
  • Postmoogle quests
  • Ordinary yellow sidequests! A lot of those were fun and interesting
  • Those chains of sidequests that start with blue Aether Current quests
  • Seasonal events -- sure, some of these wouldn't make sense in New Game Plus (like the ones that require you to defeat specific seasonal FATEs or instances), but most of them are just running around and talking to people
  • Studium and Crystalline Mean storylines
  • Custom Delivery sidequests