And explain why, of course.
Please restrict yourself to persons both real and living. Jed Clampett is not eligible because he’s fictional; Buddy Ebsen because he’s dead.
Patrick Stewart, just for the riveting State of the Union Address.
Anderson Cooper. He’s smart, easy to look at and knows about Moles. 
Lewis Black. Smartest funny man I can think of.
Cher, because she’d take no shit and she wouldn’t die - and I don’t mean just while in office, I mean she will never, ever die.
Plus all of her speeches could be made through a vocoder.
My alternate choice is Dolly Parton, but as Dolly herself has said, “don’t you think there’s been enough boobs in the White House?”
Ever since her episode of Punk’d, I’ve been trying to get the Mandy Moore for President 2020 campaign going. I think she has mass appeal, diplomacy skills, and intelligence to make an excellent leader, and I’ve seen nothing since that has dissuaded me from that position.
Sadly ineligible. Stupid Constitution.
The OP said NOTHING about the person actually being eligible for the office, beyond not being dead.
And non-fictional, so Picard is out.
Gregory Itzin. Plenty of practice on 24, plus he has ten times the sleaze of anybody since Nixon. Ought the be a fun few years (way short of four, no doubt).
I stand corrected. In that case, would George Soros be too far out of line? He is an author, after all. 
But Patrick Stewart is in, damn it!
Teller. Utterly brilliant man with sensible political opinions.
(Penn Jillette as VP. Or maybe Press Secretary.)
Hey, how 'bout Al Franken! That might actually happen.
Catalina Cruz. It’s about time we get a good looking cocksucker in the White House*
- with apologies to Robert Anton Wilson
I hear Jaden Smith is getting pretty popular.
Hulk Hogan for president!
But Sir Patrick Stewart is British, so you’d get about 10 million southern fuckwit’s protesting that he must own BP and be responsible for the Gulf oil spill (bet he hasn’t got any shares in Halliburton…)
Hence, like “Arnold”, he’s still ineligible.
Nah! Just go for Sarah Pallin. You just know that she’d talk a load of shit, but you could have pervy MILF thoughts of her in fishnet lagging while cracking a wank :smack:
/vote
I suspect he would be highly incensed should he ever end up being the First Gentleman, though.
Which makes the thought even more fun.
Carmen Elektra because she would look good delivering the speeches in a bikini.