Go to limsa lominsa, it will lead you to Aleport where you'll pick up the quest to do your first dungeon. That zone also has about 6 quests to do while you're waiting on the duty finder to pop.
Have you done all your guildhests and hunting log entries up to this point? They provide HUGE xp for what they are. Also, just go to western, eastern, and central thanalan and look at the map. I found plenty of quests that the game doesn't even point you to just by doing this. You'd be surprised what you can miss.
After limsa, it will send you to gridania to do another dungeon, but there aren't any additional quests there that I found around my level.