Learn French: Le guerrier se demande où chercher dans le donjon. - The warrior wonders where to search in the dungeon.

This is an indirect question! When the person wondering is the same person who will perform the action, you can use a question word (like où, comment, or que) followed directly by an infinitive. Où chercher perfectly translates to "where to search".

Why is it se demande instead of just demande?

Demander by itself means "to ask" (someone else). When you make it reflexive—se demander (literally "to ask oneself")—it translates to "to wonder". Therefore, Il se demande means "He wonders".

If chercher means "to look for," why isn't there a word for "for" in the French sentence?

The verb chercher already includes the idea of "looking for" or "searching for". You should never use pour after it. In this sentence, it just translates as "to search," but the rule applies: no extra preposition is needed!

Is donjon exactly the same as the English word "dungeon"?

In fantasy games or stories, yes, un donjon is a dungeon. But in real-life history, a donjon is a castle's "keep" (the main, most heavily fortified tower), which was usually above ground, rather than an underground prison!