Welcome to the game, Flaco!

As Liquid and Robert suggested, the main storyline quest will send you to Uldah around level 20-25. From there, main storyline and class quests will send you to Gridania, Mor Dhona, and Coerthas. So if you follow the main storyline, you'll get to most areas eventually. (Although you'll still have to do some exploring on your own to get all the aetherytes that exist.)

But if you enjoy exploring, there's no reason you can't start exploring now. And if you attune at each aetheryte along the way, you'll be able to teleport there next time. You jump on the ferry in LL -- bring a fishing pole or some crafting leves so you'll have something to do on the ride, although if there's a lightning storm, you can just watch the lightning -- which lands you on at the ferry dock in Thanalan. The road from the ferry dock to Uldah to Gridania is usually safe. That trip used to be a little difficult, especially with a few jerk antlings that were stationed right on the road heading into Gridania. But I think they've cleared most of that path of nasty aggroing mobs now.

Also, as Robert suggested, you'll probably want to try out the airship, which travels between the 3 main cities. You won't be able to pick up aetherytes along the way, and it costs some gil, but ... airship!

There are Battle and Crafting leves in all 3 cities. In fact, other cities have guilds for other battle and crafting jobs. The battle leves are generally pretty consistent among all three cities, but the number of crafting jobs per level is different depending on the city you're in. As a general rule of thumb, the city with the crafting guild seems to have the most crafting leves of that type. So if you want carpentry leves, you can usually find more in Gridania.

On the other hand, Coerthas and (gasp!) Mor Dhona can be more tricky. There's a higher level main storyline quest -- it's been a long time since I ran it, but I think it's around level 35 -- that requires you to travel to Mor Dhona. And there certainly used to be lots of forum posts about how difficult that quest is. The problem is that the way into Mor Dhona through Coerthas requires you to squeeze through some narrow passages, and those narrow passages used to be infested with high level mobs that aggro -- raptors, toads, boars, etc. So that run was pretty difficult, even around level 35. I know I died several times, and as a result, the quest took me around 3-4 hours to complete: run, death, respawn, run back, death, respawn, run back, etc. I don't know if that's changed, though.

If you're interested, there are some old threads posted by explorers with screenshots of some really cool areas they found hidden in little corners of the maps. So there are some gems out there, if you like exploring.