Punctuating a Sentence Containing a Question

If a sentence contains a complete question, but ends with a statement, should it be punctuated with a question mark?

Example:

Could she go to the store, he wondered

Solution 1:

I assume you do not want to put the question in quotes, as if the character were saying it, thus:

"Could she go to the store?" he wondered.

If you want to describe him thinking, then you could put the thought in italics:

Could she go to the store? he wondered.

Or you could rephrase the sentence:

He wondered if she could go to the store.

It is always possible to rearrange/reformat a sentence to avoid putting a question mark where you don't want it, as well as avoid saying a question with no question mark.