Whether you need the word 'to' in the sentence - Which place do you want to go to?

You're right, (2) is incorrect, and the reason is that the rule of Wh-Question Formation starts from a statement

You want to go to which.

then Subject-Verb Inversion and Do-Support puts the do before you and which before do, leaving to at the end.

Which do you want to go to?

Without the to at the end, however, the question would have to come from an ungrammatical sentence, since go does not take a direct object. The to is necessary as a direction for go.

(Parenthetically, thank you for mentioning that you're a native speaker. We get a lot of questions where it's not clear, and it makes a difference.)