I'd add the John Hewitt to that list. Decent enough selection, and the food is lovely, often with an interesting fish special. It's my usual spot for lunch when I'm up working in Belfast. It's also non-profit, owned by the Belfast Unemployed Resource Centre next door.
They do have live music some evenings, but it's quiet
during the day.
Only other spot in the centre I can think of is the Garrick. It's a busy enough spot at night though.