I own a small agency but don't want to run day to day or team. Should it be a GM, Business manager, other?
This is a great question and a situation I've faced a number of times.
Start with your own strengths, where you add value and where you want the business to go.
Then build out what you don't want to do, what you want to keep control of and what your ideal person looks like.
From experience I'd say that you need 2 people to run the agency - one who's operational and the other who's in charge of client strategy and client relations.