Sorry about that title but that’s how it all fit.
I’m still pondering my answer to this question myself. My initial response was Kilgore Trout, but well, I think I know what a day would be like with him. One person with off the wall ideas is enough. I think I’d like to go somewhere that I’d never been, maybe another planet, one with water. I don’t want to fight monsters or demons, mostly I’d like to have a nice lunch and take in a show.
I would like to spend the day with my literary agent anywhere with nice bowling alleys, including lunch in the snack bar.
I’m torn between Hagrid and Falcor.
My mood could change, but right now I’d be partial to Brown Dog from the Jim Harrison novellas.
Sam Weller.
Anton Chigurh. Maybe my last day.
After considering Madame Bovary, Lolita, O, and Tralala from “Last Exit to Brooklyn”, I think I’ve settled on Messalina from Robert Graves’s “Claudius”.
Or maybe the White Whale.
I’m on the same wavelength, there, but Messalina was far too um, voracious. I’d happily settle for Katy, the Hop-merchant’s errant wife from The Good Soldier Svejk. Actually, if it had to be in public, Svejk himself wouldn’t be bad. No shortage of anecdotes…
Then again, Thomasina Coverly seems likely to be an agreeable companion.
I’ve recently been reading some plays by Mark Ravenhill. There is nobody in there that I would be comfortable even sharing an elevator with. 
Mark Twain…
Bono
My first thought is Q from Star Trek The Next Generation. It is sort of cheating, because if Q is in a good mood, it is like wishing for more wishes. Though if Q is in a bad mood, oops.
In real life, maybe Ben Franklin. Brilliant guy, and am sure he would love to ask questions about the future, and Ben also knows how to have a good time.
Q who? There’s Q and then there’s Q.
OK. I’m settling on an answer for now. Hugh Conway, while he’s in Sangri-La. Not the 1937 black and white movie version either, the 1973 movie version along with the book version.
And don"t forget Q:
She also played a Klingon and a Vulcan in other episodes.
And Q too.
I did not realize there were so many Qs.
From
http://www.bbc.co.uk/cult/st/tng/q.shtml
Q A maverick member of the mysterious and powerful Q continuum, boasting an IQ of 2005 and God-like powers, Q first appeared in the Next Generation pilot episode ‘Encounter at Farpoint’.
Q, as played by John DeLancie, went on to become a popular semi-regular character in the series, appearing on the Enterprise to test the resolve of the crew by placing them in situations both whimsical and dangerous. Q introduced Picard and his crew to the Borg, and also to the legend of Robin Hood. And he was responsible for pitting Picard against a deeply unhelpful anti-time phenomenon in the classic farewell episode of the Next Generation, ‘All Good Things’.