You really can’t compare Norwich to the likes of London, Birmingham and Nottingham, it’s tiny in compassion to those, so naturally won’t have as much.
I’m not sure I can add anything to what other people have suggested unfortunately as we’re 13 miles outside of Norwich so don’t spend a huge amount of time there with the kids, but there’s been lots of suggestions, like a PP suggested, I would make a list of all the free stuff and rotate those and then add in the odd paid thing.
Not in Norwich, no and not all free, but we are so lucky in Norfolk with attractions for kids, DH’s family are from Oxfordshire and whenever they visit they never stop going on about how much we have here for children compared to where they are. Petits, Wroxham Barns, dinasour park, bewilderwood, Pensthorpe, How Hill, Holt Country Park, Yarmouth pleasure beach, Hemsby arcades/ funfair, Thrigby Hall, Amazon Zoo, Banham Zoo (sorry, just remembered you don’t like zoos 🙈) 3 National Trust properties around Norwich (they all have free stuff to do for children, granted though, a lot is in the holidays) I guess what I’m saying is, if Norwich lacks slightly, it’s kind of compensated for in other areas.