Manchester's city centre is small — you can cross it in twenty-five minutes — and a visitor who stays inside it sees a fraction of the place. The tram network and a handful of short bus rides open up the rest, and the rest is where the city is least like anywhere else.
These six are ordered roughly by how far they are from the middle, and every one of them is reachable and back within an afternoon.
Castlefield, where the canals start
Castlefield is a ten-minute walk south-west of Deansgate and it is the oldest and strangest part of the city. It holds the reconstructed gatehouse of the Roman fort the city takes its name from, the terminus of the Bridgewater Canal, and a stack of Victorian railway viaducts crossing overhead — brick, iron, and one of them now carrying a raised walkway.
The basin below is where the canals meet, and on a dry evening the towpaths and the pubs along them are as pleasant as anything in the centre. It is also the clearest single illustration of what Manchester actually was: a Roman crossing that became a canal terminus that became a railway junction, all stacked in the same few hundred metres.
Ancoats, the mills that started it
Ancoats, immediately north-east of the Northern Quarter, has a reasonable claim to being the first industrial suburb in the world — mills built to steam power along the Rochdale Canal from the 1790s. Most of them are flats now, but the scale of the buildings is intact, and walking the canal from Ducie Street toward New Islington shows you the thing itself rather than a museum's account of it.
The area is also, as the food guide to the city notes, where a lot of the best cooking has settled — so it combines well with an evening rather than needing an afternoon of its own.