I love the city for all its rain and lack of beach.
A great many places have been mentioned, but perhaps not Chetham's where you can see a spot where Marx and Engels collaborated.
https://library.chethams.com/collections/101-treasures-of-chethams/karl-marxs-desk/
Little point recommending bars, cafes and restaurants as places change so fast and tastes differ. Also, now living out of town and with young kids, I am out of touch.
Your son will be near Imperial War Museum North of course. Not massively my cup of tea but horses for courses... Just across from OT as well, so there's always the museum/stadium tour as well as match days. I'm there pretty much all home games so happy to advise if any questions.
Again in the locality, the Lowry gets a good selection of performers/acts. The Lowry Outlet is largely a waste of time.
Music venues... Many have been mentioned and it really is worth trying to take in a good range. Band on the wall, night and day, deaf institute, Albert Hall, new century Hall, ritz, Gorilla, matt and phreds, and many many more.
Maybe Warehouse Project will be more his thing? Worth a look if so.
Afflecks Palace too, whilst we're in the Northern Quarter. Ancoats too, altho that's being presented as the new 'edgy' city centre living... if edgy is yuppie coffee shops and gourmet pizza places. Long from the days of looking over your shoulder walking to Sankeys.
I enjoy plays and feel the city doesn't have the range and diversity it should have and used to have. It's good, just not good enough imo. I find the selection and quality a step down from the days of Cornerhouse and library theatre - not purely about their merger into Home, as I feel the same about the exchange in recent years.
It's a great city. I've spent decent amounts of time in many UK cities, and whilst I like lots of things about many of them, Manchester is home.