These are the things I’ve taken small children to in Manchester that they’ve absolutely adored:
Tram from St Peter’s Square to Salford Quays. Walk along the canal side (clean, safe, pedestrianised) and over the bridge to lmperial War Museum.
The Lowry - check for children’s shows, but visually fascinating either way.
Royal Exchange Theatre. Great if there’s a suitable show on - but the interior of the building is amazing on its own.
John Ryland’s Library - fascinating building, can feel like an adventure to walk around or sit in.
Manchester Art Gallery - great spaces and art and dedicated Clore gallery for children.
Manchester Museum - huge and magnificent and fun to wander around.
Whitworth Gallery - small and very beautiful; breathtaking art, glass walled cafe and wonderful outdoor spaces.
Science and Industry Museum - worth repeated visits. So much stuff.
National Football Museum - some impressive exhibitions and interactivity.
In short, Manchester doesn’t have the unmissable outdoor spaces of, say, Liverpool - but if you know where to look its buildings and interiors are truly rewarding to visit.
Lots of new places to eat have sprung up since I was last there - others can recommend.