For most of its length, the Wear takes a north-easterly course through Durham. But towards the end of its wend, the river swerves west and south to loop around an outcrop – like a finger clawing at the Ordnance Survey map.

The fingertip is the heart of Durham City, an ideal place to begin a trio of walks that show how heritage and landscape fuse seamlessly in these parts. It's a city that's at its most atmospheric draped in the half-light of dawn or dusk, when the architecture stands in sharp silhouette to the soft haze rising from the Wear.

On Palace Green you can see why the city was a shoo-in for Unesco's World Heritage List. To the south, the grand cathedral, which has helped spirits soar since the 12th century, while the body of St Cuthbert, patron saint of northern England, has attracted pilgrims for even longer, as a Saxon cathedral devoted to him originally occupied this site. On the opposite side of Palace Green stands Durham Castle, which boasts Norman foundations and scholarly occupants: it is now the most sought-after hall of residence in the nation, filled with students from for the city's University.

The first walk is a stirring warm-up: head down the cobbles of Saddler Street, make a sharp right, and below Elvet Bridge you'll find a footpath that winds clockwise, leading for a mile along a wooded riverbank barely scarred by modernity.

By the time you reach Framwellgate Bridge, just 300 yards away from where you began, you're squarely back in the 21st century. Across the bridge is the bus station, where you can embark for Barnard Castle in the Durham Dales – of which only a skeleton remains. Just half-a-mile from this market town's centre stands northern England's most remarkable museum.

John and Joséphine Bowes made an odd couple: he, an aristocratic Londoner-turned-Durham coal baron, she a Parisian actress. They turned to France for architectural inspiration to create The Bowes Museum, a formidable hillside chateau. The collections of antique furniture, tapestries and Spanish masterpieces are always worth seeing, but on this visit I focused on the new exhibition: Rokeby: Poetry and Landscape; Walter Scott and Turner in Teesdale (to 28 April), celebrating the bicentenary of Scott's Rokeby.

Scott's tale of Civil War England set against the landscapes of the Durham Dales coincided with JMW Turner's increasingly profound love affair with the county. Invited back by Scott, the artist sketched and painted several of the locations in the poem. "Distant and high, the tower of Bowes/Like steel upon the anvil glows"; after you have viewed the inspiring landscapes, you can see how scenery became poetry by wandering through it.

You can wander for a morning through countryside carved neatly by dry-stone walls. Rushing water is the constant aural backdrop. At the Dairy Bridge, just above the "meeting of the waters" between the Greta and the Tees, you can gaze down through a tunnel of trees to limestone slabs etched by time. Peek into Rokeby Park, where the mansion of the poem's title still stands proud. End at Egglestone Abbey, where "the church's ample bound" provided the backdrop for the poem's finale. Today only haunting fragments remain.

Get back on the road through the Durham Dales and North Pennines Area of Outstanding Natural Beauty to the village of Newbiggin. Stone cottages huddle around the oldest Methodist chapel in continuous use. Along the road is Bowlees, and another rather grand Methodist chapel. This one, however, is about to open as the Bowlees Visitor Centre, and also marks the start and finish of a new walk dedicated to the "Teesdale Bard", Richard Watson.

"This land is like a sponge," said Neil Diment, who devised the Richard Watson Trail. "To think that all of this was dug up by hand, by the lead and silver miners," he mused, pointing to a heap of spoil the size of The Bowes Museum. Today, this valley provides fine views up to the Pennines, and down to the "Verdant banks of Tees" that Watson described. Lead mining was a brutal, filthy occupation, and while his poetry might be no match for the Stratford Bard ("After a meal and a short rest, I find/Myself refreshed, and more for work inclined"), this seven-mile commute across these austere hills helps you to understand the human stories buried in the Durham Dales.

Over the fells and far away, the bells of Durham Cathedral toll six o'clock, which by coincidence is the ideal moment to step into The Shakespeare at 63 Saddler Street. Some say it is the most haunted pub in Durham, but whatever the spirit level, it is the ideal place to contemplate on a city, and county, where landscape and heritage converge.

Getting there and around

The best approach is by rail, with East Coast, CrossCountry and Northern Rail serving Durham and Darlington. Trains from London take just under three hours; from York the journey is less than an hour. A line runs along the coast between Sunderland and Hartlepool, calling at Seaham. Grand Central Trains from London and York serve this line.

Call 0845 748 4950 or visit nationalrail.co.uk for times and fares. Discounted Advance tickets on East Coast Trains are available through eastcoast.co.uk.

The A1(M) is the main road corridor, and roads into the Durham Dales lead west from here, while the coast is served by links from the A19.

There are bus services from Durham and Darlington to Barnard Castle, and deeper into Teesdale and Weardale. Traveline (0871 200 2233; jplanner.travelinenortheast.info) has full schedules and fares.

More information

thisisdurham.com/outdoors has details on everything from accommodation to adventure, and you can speak to the Durham Visitor Contact Centre on 03000 26 26 26, or Skype ThisisDurham. Email visitor@this isdurham.com, or text 80011, starting your message with "Visit".