Durham is the place people skip between York and Edinburgh, and then wish they had not. The cathedral and the castle share a rock in a loop of the Wear. The river walks below them — the Banks — are the right introduction, because you see the building as a person on the path would have seen it.
The city is a university town the rest of the week. It is compact, hilly, and finished in an evening plus a morning.
See
The cathedral
One of the great Norman buildings in Europe. Donation, not a turnstile, in ordinary hours. The Galilee Chapel and the cloister matter as much as the nave.
The Banks
Walk the river path from Prebends Bridge. Morning, if you can. The view is the city’s whole argument.
The castle
It is a college as well as a fortress. Tours run when the university allows. Book, or admire it from the palace green.
The market place
Down the hill, where the city buys food. A useful correction to the peninsula.