Liverpool faces the water and remembers being one of the great ports of the world. The waterfront museums are excellent and largely free. The Beatles are a real history and also an industry; take the part you want and leave the rest without guilt.
The city is friendlier than its English rivals like to admit, and smaller than the songs suggest. You can do it well in a night and a day, especially on the way to north Wales or the Lakes.
See
Museum of Liverpool and the waterfront
Start here for the city itself, not only for the ships and the band.
Tate Liverpool
A serious collection in the dock warehouses. Check location details; the waterfront has been in transition.
A cathedral, or both
The Anglican cathedral is vast red sandstone. The Metropolitan cathedral is a concrete lantern. They face each other up Hope Street, which is the walk.
A neighbourhood hour
Baltic Triangle for the newer city, or a local pub off the main Beatles axis.