The weekly challenges are well worth keeping an eye on, as are the daily hunts. Even the Levequest weekly can be a nice boost since you can do the 5 Levequests in Gridania or something to get a nice pop of XP in 5 minutes. Add in Beast Tribes and the occasional XP boosted FATE once in the StormBlood and ShadowBringers level range while you're waiting for a cue to pop.

Also consider Squadrons (or, later, Trusts). Yes they are slower than player groups to run but they're also instant cue and can provide a pretty nice XP amount based on your level and which one you do.

And, of course, at low levels it's always worth doing your job/class specific combat logs. The XP you get from completing them doesn't seem like much but it really adds up.