It's not likely the reporter is the person running for mayor.
"Ms. Ito," asked the reporter, "are you going to run for mayor?"
I'm an American, so I'd put all the commas inside the quotes. I don't remember how this works with BrE. Some people will tell you that you don't need the comma before or after the name of the person you are addressing (Meg, I saw your dog) but I think they add clarity in situations like this. If the question is a direct question inside the quote, then put the ? inside the "
1. Tony said, “Meg, I saw your dog in Kevins Yard“.
2. “Julio, the telegram is for you”, called his brother.
3. Mr. Simpson asked “What time does the softball game begin?”
4. "Ms. Ito," asked the reporter “are you going to run for mayor?"
5. “Our company is on McNeil Road,” replied the receptionist.
6. “You need to improve your defense,” said Coach Diaz, “if you expect to win the game“.