Every city has a handful of starting quests you can do that'll get you a couple levels from the start. You have Hunt Logs, FATEs and Levequests until level 10, you can do Guildhests at level 10 (not worth spamming past the initial clear/daily roulette though) and once you get to 15 you can do Dungeons and incorporate the prior methods. Once you're level 16 you'll have two dungeons available to you and will be able to do the daily low level dungeon roulette as well.