Chester is the most intact walled city most English people have somehow not put on a first itinerary. The wall is a full circuit, about two miles, and it is the right way to see the place. The Rows — covered galleries at first-floor level — are medieval shopping streets that still work.
It sits on the way to north Wales. Conwy and the Eryri are the continuation if you have a second day. Chester alone is a rich afternoon and a morning, not a week.
See
The walls
Do the circuit. The eastgate clock is the famous bit and the least interesting ten yards. The river section is the best.
The Rows
Walk the upper level on Watergate and Eastgate. Go into the cathedral close when the shops have done their job.
The cathedral
A choir school and a cloister, quieter than the walls. Worth the ticket if you like church woodwork.
The river
The Groves, below the wall. A short extra if the circuit has not finished you.