Hmmm, little kids in city centre...
Whitworth Park (and gallery) not too far down Oxford Road on the bus. Don't know if it has a play area though. Platt Fields (coupla miles further one in bus/taxi/car) is huuuuuuuuuge and will have lots of stuff. Always used to have play equipment, lake, animals - dunno what these days though.
Triangle/Exchange Squares near the Cathedral and Urbis museum very nice for little ones to run around - not a park as such but if it's nice weather you can while away lots of time here...
Aquatic Centre is closest swimming, again down Oxford Road. Manchester Museum (at the University) just beyond there also - dinosaurs, animals, mummies etc.
Lots of galleries which have child-friendly bits usually: City Art Gallery on Moseley Street has great interactive stuff for kids. Cornerhouse (Oxford Rd again!) gallery, decent cafe
Albert Square and St Peter's Square also good for running about
Get on the tram from centre to Salford Quays for running around spots, boats, bridges. Lowry Centre (theatre/gallery) often has kids' activities and art carts etc.. Imperial War Museum here probably a bit old for your kids but outside spaces nice
Do an open top bus tour: yes, even in Manchester.
Some great blue badge walks if your kids like walking.
Science and Industry Museum as others have said is great and you can fill lots of hours here.
If I think of any other good ideas, will post.