There is only one Manchester... Not Greater Manchester... But THE City of Manchester.
Bolton, Salford, TRAFFORD (LOL XD ), Wigan, Stockport, Bury, Rochdale, Oldham and Tameside are all outside of Manchester.
City Centre (M1)
Moston
New Moston
Hulme
Moss Side
Miles Platting
Ancoats
Newton Heath
Gorton
Didsbury
Whythenshawe
Clayton
Fallowfield
Rusholme
Northenden
Harphuray
Ancoats
Ardwick
Chorlton
Levenshulme
Prestwhich
Whitefield
Crumpsall
Cheetham Hill
Blackley
Openshaw
Beswick
Longsight
Whalley Range
Abbey Hey
Burnage
Withington
Baguley
I think that's all of the actual Manchester towns. Hope that's what you were looking for.