I'd say start at Wanderer's Palace. It's the easiest non-story 50 dungeon and very doable in AF1 gear. It currently gives 100 Tomestones of Philosophy and 30 Tomestones of Mythology. This Philosophy Tome number is equivalent to Amdapoor Keep, Castrum Meridianium, and the Praetorium. The two story instances are relatively speed run friendly, so you'll be considered a drag on many groups due to not having a bunch of Darklight yet, and AK should not be attempted without some Darklight and gear from Wanderer's Palace.

Another thing you can and should go for immediately is unlock Ifrit Hard Mode and get your "Ifrit's <weapon>" from it. Even Duty Finder groups practically have this one down to a science, so just listen to the party and rip him a new one