Visit Kelham Island Museum and see the River Don Engine, the 12,000-horsepower steam engine of 1905, and the Bessemer converter

Tour Abbeydale Industrial Hamlet, the 18th-century water-powered scythe works

Explore the Millennium Gallery and its Winter Garden in the city centre

Kelham Island Museum keeps the River Don Engine, a 12,000-horsepower steam engine of 1905, and a Bessemer converter, the last to work in Britain, brought from Workington. South of the centre, Abbeydale Industrial Hamlet is an 18th-century water-powered scythe works, and in town the Millennium Gallery stands beside the Winter Garden.

Sheffield: Kelham Island and Abbeydale

Climb or walk under Stanage Edge, the gritstone escarpment above Hathersage

See North Lees Hall below Stanage Edge from the footpath, the house thought to have inspired Thornfield Hall in Jane Eyre

Walk the Longshaw Estate, National Trust moorland and woodland

Stanage Edge is the long gritstone escarpment above Hathersage. Below it, North Lees Hall is thought to have inspired Thornfield Hall in Jane Eyre, and east of the village, above Padley Gorge, the Longshaw Estate is National Trust moorland and woodland.

Stanage Edge and Hathersage: The House Behind Thornfield

Tour Chatsworth House, the Cavendish seat since 1549

Walk the gardens and park beside the Derwent

Cross Bakewell's five-arched bridge over the Wye, built in the 13th century

Eat a Bakewell pudding in the town where it was created

Chatsworth, the seat of the Dukes of Devonshire, has belonged to the Cavendish family since 1549; Bess of Hardwick began the first great house here in 1553, and the 4th Earl began rebuilding it in 1687. It stands on the east bank of the Derwent in parkland under wooded hills, with gardens remade by the 4th Duke in the 18th century. Four miles south-west, Bakewell, a market town since 1254, crosses the Wye on a five-arched bridge of the 13th century and is best known for its pudding.

Chatsworth and Bakewell: The Cavendish House and the Pudding Town

Walk into the entrance of Peak Cavern, the largest cave entrance in Britain — described by William Camden in 1586 as the Devil's Arse, and one of Thomas Hobbes's Seven Wonders of the Peak in 1636; ropemakers lived and worked inside it until 1915

From the summit of Mam Tor (517m), walk the ramparts of the hill fort and look down on the landslips of the eastern face — the Shivering Mountain — which closed the A625 road for good in 1979

In Castleton, find a piece of Blue John, mined for ornaments in the 19th century and still dug on a small scale

Walk the broken road under Mam Tor that the landslip destroyed

Castleton sits under Mam Tor at the head of the Hope Valley with four show caves around it. Peak Cavern, described by William Camden in 1586, has the largest cave entrance in Britain; Mam Tor above it is crowned by a late Bronze Age and early Iron Age hill fort and slides steadily downhill, taking the old road with it; and Blue John, the banded purple and yellow fluorite, is found in Britain only at the Blue John and Treak Cliff caverns here.

Castleton: Peak Cavern, Mam Tor and Blue John

Walk or cycle the Monsal Trail, the old Midland Railway line through the Wye valley

Cross the Headstone Viaduct and look down on the Wye

Ride through the tunnels reopened in 2011

Look down on the viaduct from Monsal Head

Find Cressbrook Mill and Litton Mill beside the trail

The Midland Railway built its line through the Wye valley in 1863 to link Manchester with London, and after it closed in 1968 the trackbed became the Monsal Trail, opened in 1981: 8.5 miles from Topley Pike, east of Buxton, to Coombs Viaduct beyond Bakewell, past Chee Dale, Millers Dale, Cressbrook and Monsal Dale. It crosses the Headstone Viaduct below Monsal Head, passes Cressbrook and Litton mills, and runs through six tunnels, reopened to walkers and cyclists in 2011.

The Monsal Trail: Headstone Viaduct and the Tunnels of the Wye

Walk the 500 acres of Yorkshire Sculpture Park, opened in 1977 in the Bretton Hall estate, among works by Henry Moore, Barbara Hepworth, Andy Goldsworthy and James Turrell

Visit The Hepworth Wakefield, David Chipperfield's gallery opened in 2011

Find the Henry Moore bronzes in the open landscape at YSP

Walk the lakeside paths and visit the Underground Gallery at YSP

The Yorkshire Sculpture Park opened in the Bretton Hall estate in 1977 and spreads Moore, Hepworth, Goldsworthy and changing shows over 500 acres of park, lakes and pasture; it is the only place in Europe to see Barbara Hepworth's The Family of Man in its entirety. Seven miles away in Wakefield, David Chipperfield's Hepworth gallery opened in 2011 on the Calder, holding Barbara Hepworth's plasters and prototypes.

The Yorkshire Sculpture Park and the Hepworth

Walk up onto the Kinder plateau from Edale

Find the trespass plaque at Bowden Bridge quarry

Walk to Kinder Downfall on the western edge

The A57 over Snake Pass opened on 23 August 1821 at a cost of £18,625 and was then the highest turnpike road in England; it is often shut by snow and has been closed for months at a time by landslips. South of it rises Kinder Scout, where on 24 April 1932 Benny Rothman and the British Workers' Sports Federation walked deliberately onto private moor. Some of the trespassers were jailed, and the public outcry that followed made the trespass a symbol of the long campaign for open access that ended with the right to roam in 2000.

Snake Pass and Kinder Scout: The Trespass That Opened the Hills

Walk the deserted medieval village of Wharram Percy, abandoned by about 1500

Trace the house platforms and the fishpond at Wharram Percy

Walk a section of the Wolds Way through the dry chalk valleys

The Yorkshire Wolds Way runs 79 miles of chalk from Hessle on the Humber to Filey Brigg, opened in 1982 and one of the quieter National Trails. Beyond Thixendale, about three-fifths of the way along, lies Wharram Percy, the deserted medieval village abandoned by about 1500, where the church shell stands in an empty valley with the house platforms still visible in the grass.

The Yorkshire Wolds Way: Wharram Percy and the Chalk Valleys

Walk the reedbeds and lagoons of Far Ings National Nature Reserve at Barton-upon-Humber

Look up at the Humber Bridge from the Far Ings reedbeds

Watch migrating waders and wildfowl from the hides

Far Ings, on the south bank of the Humber at Barton-upon-Humber, is a national nature reserve of reedbeds and lagoons in old clay pits, just west of the Humber Bridge. The estuary funnels migrating birds down its shores, and the hides look out over waders and wildfowl.