Four days in Aarhus: a circular rainbow on the roof, and a murdered man from the Iron Age

The cathedral is a hundred metres from the main square and is the longest and tallest church in Denmark, which for a building begun in the twelfth century and finished over the following hundred years is not a small claim. Inside it is white, high and unusually plain, with the exception of a five panel altarpiece by Bernt Notke of Lübeck from the 1470s and a set of medieval frescoes that were whitewashed over at the Reformation and uncovered again in the twentieth century. The tower can be climbed.

In the afternoon walk ten minutes to ARoS. The permanent collection runs Danish golden age painting through to contemporary installation, and the nine black walled rooms in the basement are worth the visit on their own. But the reason people come is on the roof: Olafur Eliasson's circular glass walkway, a hundred and fifty metres round, glazed in every colour of the spectrum in sequence, so that walking it turns the entire city red, then orange, then yellow, and so on the whole way round.

Go up an hour before the museum closes. The low light is what makes it work, and the crowds have gone.

Den Gamle By is not a reconstruction. It is seventy five actual Danish buildings, dating from 1597 to 1909 and taken down in towns all over the country when they were about to be demolished, rebuilt here into a coherent market town with cobbled streets, a millstream and working shops. A merchant's house, a mayor's house, a mint, a bakery. There are staff in period clothes but not oppressively many, and they will talk to you about the work rather than perform at you.

The part most people are unprepared for is the twentieth century section. Two further quarters have been added, one set in 1927 and one in 1974, with a jazz club, a record shop, a hairdresser and a fully furnished flat in each. The 1974 apartment, with its brown kitchen and its cassette recorder, does something to visitors of a certain age that the seventeenth century houses do not. There is also a small flat set up as the home of a woman with dementia, used for reminiscence therapy, which is unexpectedly moving.

Allow three hours minimum and eat inside; the bakery and the 1920s coffee house are both real. Afterwards, the botanical garden is immediately next door: hilly lawns, ponds, and a glasshouse complex with a tropical dome you can walk up inside on a spiral ramp. It closes later than the museum and costs nothing.

Moesgaard is seven kilometres south and the single best reason to come to Aarhus. The building, finished in 2014, is a huge wedge driven into a hillside with the roof planted in grass and sloping down to meet the ground, so that people picnic and in winter sledge on top of the museum. Inside, a wide staircase descends through human evolution, with life sized reconstructions of hominins standing at the landings.

At the bottom are the two things you came for. Grauballe Man was found in a peat bog in 1952, died around the third century BC with his throat cut from ear to ear, and is the only bog body anywhere preserved completely, down to the hair, the stubble and the fingerprints. Next to him is the Illerup Ådal deposit, thousands of weapons from a defeated army thrown deliberately into a lake as a sacrifice, laid out across a whole wall. Between them is a reconstructed Bronze Age burial mound you walk inside.

The parkland below the museum runs down to the beach and is free and open all year, with reconstructed prehistoric buildings along the way and a run of woodland to the sea.

Coming back, get off in the Marselisborg forests. The deer park is a fenced section of the woods where fallow and sika deer wander loose and will come close, open from dawn to dusk and free. The royal family's summer residence is a couple of kilometres further, a modest white house whose gardens are open to the public whenever the monarch is not there.

Two last things, both near the station.

In the basement of a bank across from the cathedral is a single room of Viking Aarhus, made from what was dug out of the foundations when the building went up: the town rampart, part of a house, pottery, a skeleton. It takes twenty minutes and it is where the city's name comes from. Aros, the river mouth, was a fortified settlement here by about 900.

Then walk down to the water for Dokk1, the public library at the harbour front, which is the largest in northern Europe. Calling it a library undersells it: it is the city's living room, with a children's section that is essentially a playground, a robotic underground car park, and a bell that rings across the harbour every time a baby is born in the Aarhus hospitals, set off by the parents from the maternity ward. Sit on the steps outside with a coffee and watch the water.

The station is five minutes from the door.