Manchester's most underrated quality as a base is its position. It sits in the middle of the densest rail network outside the south-east, which means a traveller who books four nights here can reach a startling number of genuinely different places and come back the same evening.
That matters more than it sounds. The alternative — a night in each of four northern cities — costs you two half-days to packing and check-in for every move. Basing yourself in one place and going out from it buys back most of a day.
Here is what is actually within reach, in order of how easy it is.
Liverpool, fifty kilometres west
Liverpool is the obvious pairing and the one most visitors underestimate, because the two cities are spoken about as rivals and are assumed to be alike. They are not. Manchester is a nineteenth-century industrial city that turned inward — mills, warehouses, canals. Liverpool is a port that faced outward for two centuries, and it shows in the architecture, in the accent, and in the fact that its grandest buildings are all pointed at the water.
Trains run frequently between the two city centres and the journey is short — under an hour on the fast services, and among the busiest inter-city routes in the country. It is comfortably a day trip in either direction.
What to do with the day: the Albert Dock and the Three Graces on the waterfront, the two cathedrals at opposite ends of Hope Street, and the Walker Art Gallery. If you have any interest in the Beatles at all, this is where that is, and it is treated seriously rather than as a novelty.