I have never tried this build, so i think i'm going to:

Major skills are Light weaponry (includes unarmed in SkyRe) and Alteration.

Minor skills are sneak and restoration. Maybe a bit of illusion...

No armor, using Alteration Master Robes, because they look so cool and fits him.

I don't know what should i do with this character, that's i'm asking you.

Maybe live peacefully in the wilds? I don't know. What do you think?

Shouldn't a monk wear monk robes? There's both hooded and normal types.

I would say help out temples, there's the quest to spread the love from Riftens temple which is a non violent quest if you're playing a pacifist. If you don't mind being a martial monk then help the 1 in Dawnstar deal with the nightmares.

Something different that you could do is wear robes then when a fight or serious situation happens, throw off your robes and wear ragged trousers so it's like you're wearing pants underneath and stuff just got serious

I want to try a Monk build, but a Monk as in that OP, incredibly awesome job in Final Fantasy.

Probably will never work, though, considering the lack of unarmed skill.

I can't think of any reason why a monk wouldn't want to put a stop to the dragon or vampire attacks.

So I think in addition to the temple quest's you could also do the main quest and the dawnguard quest.