Birmingham

Wrapped in layers of gold and silver rings, the library opened in 2013 and is free to enter. Roof gardens on the 3rd and 7th floors look out over the centre. The top floor holds the Shakespeare Memorial Room, moved over from the old library.

A curved building clad in 15,000 aluminium discs closes off the end of the Bullring shopping centre. The store opened in 2003, and the discs pick up the sky, shifting colour with the weather. The steps of St Martin's church just below frame the whole building.

Several canals meet at this basin right in central Birmingham, long thin narrowboats moored along its edge. The city likes to say it has more miles of canal than Venice. Following the towpath, you can cross the centre with hardly a road to cross.

Hundreds of jewellery workshops crowd this district, which turns out a large share of Britain's jewellery. At the Museum of the Jewellery Quarter the owners shut the factory in 1981 and left, tools still on the benches. You see it with a guide.

Workers' houses built back to back, sharing a rear wall, around the last courtyard of its kind still standing. You pass through rooms dressed for each era from the 1840s to the 1970s. Entry is by guided tour only, and it needs booking.

A chocolate attraction set beside the Cadbury factory in Bournville. You taste melted chocolate on the spot and leave with a few bars in hand. Tickets are sold for timed entry, so in school holidays a visit needs booking.

Moving their factory here in 1879, the Cadbury brothers built a planned village for the workers. It got big gardens and green space, and in line with the Quaker brothers' views no pub was allowed. On set days the carillon by the village green rings.

A small gallery in an Art Deco building on the University of Birmingham campus, and admission is free. A handful of rooms hold Rubens, Monet and Van Gogh, so an hour covers it. Outside, the university's red-brick clock tower, Old Joe, is right in view.

The Digbeth factory that made Bird's custard powder now houses studios, shops and bars. Graffiti covers the railway arches and lane walls around it, and the pieces keep changing. Markets set up by day at weekends, and at night the warehouse clubs fill.

An open-air museum in Dudley, to the west, with a coal mine, a canal and a rebuilt street of old shops. Peaky Blinders was filmed here. An old-style shop on the street fries fish and chips the period way, and the queue gets long at lunch.

The free civic museum beside the Council House on Chamberlain Square. It owns more Burne-Jones than anywhere else, so the Pre-Raphaelite rooms lead. The Staffordshire Hoard, Anglo-Saxon gold dug up in 2009, has its own gallery.

Gardens opened in 1832 on a hillside among the houses of Edgbaston. Four linked glasshouses split tropical, Mediterranean and arid plants, and the outdoor beds step down a lawn slope. In winter the tropical house is humid enough to fog glasses on entry.

A Jacobean mansion built from 1618 to 1635, right beside Aston Villa's ground. In 1643 a Parliamentarian cannonball came through a window and door and smashed the stair banister; the damage remains. It opens in spring, summer and autumn only.

A watermill built in 1771 whose wheel still grinds flour. Young Tolkien lived close by from the age of four to eight and later named it as the model for the mill at Hobbiton. You see inside only with a guide, often followed by a walk in nearby Moseley Bog.

An early 18th-century Baroque parish church that became a cathedral in 1905. Four stained-glass windows designed by Birmingham-born Burne-Jones wash the east and west ends in red and blue. Office workers eat sandwiches on the churchyard lawn at lunch.

The science museum inside Millennium Point, beside Digbeth. As befits a factory city, steam engines and old machines are run for real, and a Second World War Spitfire hangs from the ceiling. Hands-on children's zones make weekend mornings the busiest.

A Severn gorge in Shropshire where the world's first cast-iron bridge went up in 1779, counted as the birthplace of the Industrial Revolution. Ten museums dot the valley, Blists Hill Victorian Town the largest. Allow an hour by car; buses are awkward.