Consider your sleep patterns and food intake and such, not just on the day/night but for a few days beforehand. Okay, that's how to be active for 24 hours, but run a game?
Don't ask me, I avoided even trying.
Alright, I have observations.
Nothing too intricate. That would take a lot of prep and be subject to you and the players passing out and forgetting everything. The chances that they'll recall the enigmatic phrase of the mysterious man who appeared in the first five minutes is very low, even if there's a handout in front of them.
Likewise, nothing too atmospheric. Horror from dusk till dawn might work wonderfully, but then you have till dusk again and you've had so much sugar that everything could suddenly be funny.
A milieu you know well enough to run in your sleep, as at times you may well be doing so.
Go for action and stuff. It's a good basis for many games, being able to go "sod it, ninjas attack" helps when stuck, rolling dice is a physical activity that keeps players awake, and the charity reroll is a valuable addition to the fundraising effort.
It being a milieu that can go surreal as you get increasingly wonky is a bonus.
The four that went for it this year (one of which managed the 24 if you count the power nap in the middle) were two dungeon bashes, a non-dungeon standard fantasy, and an SF zombie apocalypse with lots of explosions.
Jumping on and off points. Essentially eight three-hour sessions, or six four-hour ones, or something to that effect. You could try running a shortish campaign or series (it's been done) but episodic with a bit of escalation and a biggish final battle would be safest.
You might consider GM relays, as playing while loopy from exhaustion and artificial stimulus is less game-exploding than GMing in such a state.
Before half a dozen people offered to run games the whole day through I did consider some options, though none over twelve hours seriously.
All Night Vampire and then sleep through the day. Not seriously thought through.
Superheroes, which we had too many of already.
Buffy, which I've fallen asleep GMing once at a convention (I had a cold) so could do again. Basically superheroes, obvs.
Doctor Who And The Most Episodic Game Ever, where every couple of hours it's a new planet and century. And if somebody wants a Dalek episode they can put money in the charity reroll jar.
Uncharted because, hey, successful video game launch recently apparently.
I had my Buffy and Uncharted adventures from the Nationals ready. I halfway wrote a World Of Darkness plot but decided it was too heavy for the target audience.
But as is I played and administrated, did not GM. And not even for 24 hours. And that was tiring enough.