First instinct is to say Morello so I can bring up some of the concerns the playerbase at large has with some champions, but nobody wants to spend their day with Nerf Master Suck Town.

I'm going with Phreak, gotta get that tons of damage.

Xypherous. I'd tag along on his work for a day to get a feel for it, and ask him for the requirements for getting a job like his.

Also, he seems very wise and gentle.

Phreak, will get me laid instantly.

Ezreal. He has made some of my favourite champions, and from his posts in @Ezreal, he is extremely intelligent/into good literature. It'd be awesome to discus philosophy and jank. It'd be a great day.

I don't live that far away from Riot HQ, the idea of bringing baked gifts and showing appreciation in general has crossed my mind.

My friends and I just met a bunch of rioters briefly at MLG, considering that they all seemed at the very least somewhat entertaining, it seems unfair to choose.

Morello so I can hit him with the nerf bat!

RiotKryo is a cool dude.

This Rioter has not shown himself on the forums yet, but I'll tell you his name rhymes with "Verdict."
I would spend my day with him because he is incredibly nice and apparently a hard worker.
We would probably play League of Leagues all day.