Pie-minister on church street is good, and Sugar Junction on Tib Street sells nice cake and coffee, both are 5 minute,s away from Piccadilly as is Matt and Phreds jazz club.
if you visit the football museum, Manchester cathedral is just round the corner, which means you could then pop into Proper tea opposite for more cake.
walk down Deansgate and call in at the John Rylands library a truly fantastic building, continue up Deansgate until you reach dimitris greek restaurant turn right and the MOSI is at the bottom.
Duke street has got the remains of a roman fort, and a nice bit of green space to sit and chill.
The canal is just in front of the roman fort, if you take the rochdale canal towpath back towards Canal Street,you could call in the Richmond tea room for more cake.