The Cathedral Close is the natural starting point. Exeter Cathedral dominates the south side of the city centre, and the close around it is one of the most attractive cathedral precincts in England. Mol's Coffee House on the north side of the close is an Elizabethan timber-framed building that has been serving visitors since the 16th century.
Below the streets, the Underground Passages offer guided tours through medieval water supply tunnels — unique in England. Sections of the Roman walls survive throughout the city centre, some standing over five metres high.
The Royal Albert Memorial Museum on Queen Street is one of England's best regional museums, free to enter and covering natural history, world cultures, and fine art. Down by the water, Exeter Quayside along the Exe makes a good afternoon: old warehouses converted to cafes, kayak and canoe hire, and a pleasant towpath.