I have two very young children so if they did not come with me to Eorzea then the majority of my time would be spent trying to find a way to either get home to them or bring them to me. Regardless of the danger if that meant facing the primals and ascians and everything else to do it I would.
Otherwise I would find my Eternal Bond partner and our friends and work on making a safer world to live in. (This would include mocking my friends for their choices in character names. ^_^ ) Also exploring the world, we have airships and a ton of mounts and all kinds of modes of travel so it would be great to visit all the wonderful locations I see in game.
Oh, and search for some of the people I know from the boards and in game to say hi.
And finally prove to all the NPC's that I can actually talk not just nod my head and do whatever they say.