Off the top of my head, managers I like/rate (but who I wouldn’t necessarily want at City) are:
Mick McCarthy worked did well at Ipswich on a tight budget.
Tony Mowbray’a teams always seem to play decent stuff.
Gary Rowett’s sides always seem well organised.
Neil Warnock is a great character who revels in his pantomime villain role.
Mark Robins always comes across well in interviews.
Alex Neil - horrible football but is able to get results.
In terms of City managers, Terry Cooper is my favourite, no one else comes close. Then it’s Joe Jordan (first spell) and Cotts.