We may have a day layover in Manchester. What could we see and do there or nearby?
Football match?
The People’s History Museum if your politics are left of centre or you have an interest in the labour movement.
The Manchester Art Gallery is small but excellent
The National Football Museum if you have an interest in the sport.
The Gay Village is fun to stroll around and it is world famous . The UK Queer as Folk was set there.
I’ve been there 4 times, tell us more what you like to do.
There is plenty to see - The Imperial War Museum North, many galleries including the Lowry, several theatres, the Cathedral, John Rylands Library (a stunning building), take a guided walk and museums including the Manchester Museum, Transport of Greater Manchester and the Science and Industry Museum.
Plenty of great eateries and shopping.
One of the best music scenes in the country.
Walk round the gentrified canals of Castlefield.
We enjoy "touristy" and historical sites. At this point our itinerary may change to only 4 or 5 hours. We usually will take a city tour when in a new place.
We appreciate all the thoughtful ideas.
My top tip is to see if the Museum of Science and Industry is having a demonstration of the cotton-making process during the hours you are there. Without the demo, it's just a bunch of old machines. But the demo brings them to life (literally, as they turn them on and show how they operated), as well as what was involved and how hard and dangerous the factory work was.
Otherwise, you've gotten good lists of attractions in the posts above. Note that except for the Imperial War Museum North, just about everything you'd want to see in Manchester is in the center and is a walk (or very short taxi ride) from the train stations. Manchester Oxford Road is a bit closer walk to many things than Manchester Picadilly, if you have a choice.
Here's the direct link to the Museum of Science and Industry demonstration I referenced above. I saw the one called "Manchester Mills": https://www.scienceandindustrymuseum.org.uk/whats-on/textiles-demonstration