Ashton on Mersey Canal basin museum (not sure of exact name but it wins children's museums awards. it has lots of toy trains, also a barge trip, dressing up, etc.
Manchester Science museum has toddler section and sometimes storyteller events. this is free.
Wythenshawe park - working farm, "safari walk", and playground. all free.
Manchester city art gallery has interactive gallery with lots to push and fidget with. surprisingly good with toddlers. try a quiet time like a Sunday morning.
Styal Mill - don't go inside but there are walks by the river with a little beach for paddling. also a good cotton-mill-themed playground. that's free.
Heaton Park. working tram rides. big playground. various special events on there.
Manchester Museum. dinosaur bones and mummies, also living snakes and reptiles.
Poynton has a Garden centre with a miniature train running round it. also does pot painting etc when they're a bit older.