Either Palace of the Dead or dungeons. (Dungeons are probably faster for tanks and healers who can get quick queues. PotD might be faster for damage dealers, unless they've got friends to run dungeons with to avoid the queues.)

Either way, at least do your leveling roulette each day. When its daily bonus is available, it beats everything else (even if you do have to wait in queue a bit). You can run FATEs while waiting for the queue to pop. With the latest patch, now you can have your chocobo out to help with those FATEs while waiting on a DF queue.