Is there a way to manually type the precise pixel position for a guide, instead of zooming in and dragging it to the correct position?
Sadly, no. I've wished for this many times myself.
Michael Szalapski wrote in a CreativeCow thread,
"At 100% zoom level in the comp viewer, guides move on full pixels, so you can place them on exact pixels right where you want them if you sit them on a null (or solid or whatever). Granted, it doesn't snap, but when I tried it just now, I got it right where I wanted it pretty quickly with a null as a reference. "
That's the best solution I've ever come across. Not what you asked for, I know.
Updating my answer as this is now possible in CC 2019 onwards: Create a guide, right click on it and enter a numeric value. Simple!
I just write an "O" and align it in the middle with the align tool. Then zoom in and set the guides so there's a perfectly placed cross in the middle of the O. Hope you find this useful.
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1If you're aiming for the middle, just turn on the screen safe guides - they give you a cross smack bang in the middle of the comp ;) – Jamie Bruce Jul 10 '18 at 8:44