Toto-rak is available at 25.
Ifrit is available at 30.
There are a few NMs you can do at ~34 and trade in their drops for seals.
You can do Caravan Escorts starting at 25 or 30.
Behests are a great way to level up. I usually get 5000-7500 EXP from a solo Behest at level 25-26.
There are a lot of public dungeons you can do from 25 onward.
There are a lot of sidequests that give okay amounts of EXP (1800+) that are little more than go here talk to X, Y, and Z, and come back for reward.
There is the main quest that gives a ridiculous amount of Gil.
There are also the class quests starting at 20.