What's wrong here? "I wonder where he's gotten to?"
The past participle
Was that a little tricky? Congrats to 16% of you. You don't use a question mark with a statement that isn't a question. The word "wonder" hints at a question, but the sentence itself is not a question. There are various kinds of questions:
Do you like ice cream?
You didn't eat all the ice cream, did you?
You ate all the ice cream?
On the other hand, "I wonder" involves just a statement. Therefore, no question mark:
I wonder where he's gotten to.
As for the past participle, in America, "gotten" is the usual past participle; in British English, it is usually "got." See this link for more on the verb "get."
As for ending the sentence with a preposition, it is allowed. See this link for more info.