The ending of Final Fantasy VI is fairly concrete- it resolves the character's storylines with one or two exceptions. What happens after the end is anyone's guess, and Square-Enix certainly isn't saying. Until Final Fantasy VI becomes their latest FFVII-style cashcow, we won't know what happens to Locke, Edgar, Setzer, and the gang.
To me, the implication is that Locke and Celes are well on their way to starting a life together. I imagine that they would settle down somewhere nice and raise a family. Locke could open a shop or relic museum or something, allowing him to travel to aquire new treasures. Or maybe he'd pull a Laguna and turn to politics, after being some sort of local hero. I do not know.
Of course, some have suggested that he gets together with Terra after the end, perhaps after he and Celes have broken it off. I suppose that it's a possibility, and again I'd imagine they would settle down somewhere, probably Mobliz, and the emphasis on family would become more important than in the above scenario.
There is, of course, the third scenario, where Locke winds up unnattached. In this case I think he'd probably go travel the world again, without a commitment to tie him down to one place. He'd probably live an Indiana-Jones style life- and hey, there's footage out there of him with a whip, and I think would be happy this way too. Heck, maybe he'd do this with the help of Celes or other members of the old returner gang. There's no telling.
And then there's the question of whether he's even found closure at all. Can you really repair yourself when you were so far gone you kept your dead girlfriend preserved in a strange man's basement? Is happily ever after really an option at this point? But where there's life there's hope, he cried, and if you haven't figured out that there's no such thing as to hope in vain you haven't been paying much attention to Final Fantasy VI. If Locke doesn't manage to pick himself up again it'd be pretty thematically inconsistant, but it's fair to assume that he still has a ways to go before he graces the cover of Sanity Fair.
But I guess when it comes down to it, I don't know. And strangely, I'm fine with that.
PS, Square-Enix: Final Fantasy VI doesn't need a sequel, it was tied up pretty nicely, unlike Final Fantasy VII. What FFVI needs is high quality renders of Locke's face. If you do that, I'll even buy The Bouncer or something. Thanks.