Besides doing the main story there isn't much you can do, just doing MSQ missions with skipping cut scenes I managed to do it in around a day from the end of ARR to the start of HW.

Try this website:
https://ffxiv.consolegameswiki.com/w...cenario_Quests

This will help tell you how much you have left and while you may not like whm it is a nice way to get use to healing and such before you play ast where you have to heal, dps and worry about pulling and distributing cards.