Is there a place on earth where it is dark for 24 hours at certain times of the year? (or pretty close to that)?

Yes. Both poles the  Sun doesn't rise for more than  2 months. It also doesn't set for than 2 months. Anyone who says it's 6 months is wrong.  

It's dark in a closet for as long as you stay in there

Yes, at both poles for months rather than days. It happens during their respective winters. For those of us in the Northern Hemisphere it is the North Pole where there is continous darkness. The South Pole experiences this when for us in the Northern Hemisphere it is summer but it is winter in the Southern Hemisphere.

Yes, and more than 24 hours.

Above the Arctic Circle, 66.5 Degrees north Latitude.

During the Winter time The sun never rises from Early October until Early March.

Same down south at the south pole.

But different dates.

I'm sorry that you couldn't figure this out with the availability of Google.. you must be a bot.. moderator please ban

Near the poles at the Solstices.