Four days in Nairobi: the safari starts before you leave town

Start in the centre, which is smaller and more walkable than the city's size suggests. The Nairobi Gallery occupies a domed colonial building on Kenyatta Avenue that was once the provincial commissioner's office, known to generations of Kenyans as Hatches, Matches and Dispatches because births, marriages and deaths were all registered there. The exhibitions change constantly, so what is on the walls is a lottery, but the building and the Joseph Murumbi African collection it holds are worth the half hour on their own.

Walk down towards the Uhuru Highway to the August 7 Memorial Park, built on the plot where the American embassy stood until a truck bomb destroyed it in 1998, killing 213 people, the great majority of them Kenyans on the street outside. It is a small, well-kept garden with a wall of names and a single room of exhibits, and it is the most affecting place in central Nairobi.

Finish at the Kenyatta International Conference Centre, the tower with the saucer on top that appears on every photograph of the city. A lift and a short flight of stairs get you onto the helipad roof, from where you can see the whole sprawl, the green line of Uhuru Park, and on a clear evening the Ngong Hills to the southwest. Go in the last hour before sunset.

Leave in the dark. The park gates open at six and the first two hours are when the animals are moving, before the heat pushes everything into the shade. Nairobi National Park covers about 117 square kilometres of open grassland and river forest, fenced along the city side and open to the south, and it holds lion, leopard, cheetah, buffalo, giraffe, zebra, hippo and a well-protected population of black rhino. What it does not have is elephant, which is the one thing people expect and the one thing missing. The photograph everybody comes for is a rhino or a giraffe with the skyline standing up behind it, and it takes no skill at all to get.

Come out around ten and go to the David Sheldrick Wildlife Trust, at the park's Lang'ata edge. Orphaned elephant calves are hand-reared here until they can be released back into Tsavo, a process that takes years. The gate opens to the public for one hour a day, from eleven, when the younger calves are brought in for milk and mud and a keeper explains where each of them came from. Book online in advance, because it does fill.

After lunch, the Giraffe Centre a couple of kilometres away runs a breeding programme for the Rothschild's giraffe, one of the rarer subspecies. A raised wooden platform puts you level with their heads, and you feed them pellets, which is undignified for everybody and completely irresistible. There are warthogs underneath hoovering up what gets dropped.

The suburb of Karen is named after Karen Blixen, who ran a coffee farm on this ground from 1917 until the plantation failed and she went back to Denmark in 1931. Out of Africa, published in 1937 under the name Isak Dinesen, is what she made of those years. The stone farmhouse, built in 1912, was handed to Kenya by the Danish government at independence and became a museum in 1986, a year after the film came out. You go round with a guide, which sounds restrictive and is not: the guides are good, the rooms are furnished close to how she had them, and the Ngong Hills sit on the horizon from the veranda exactly as advertised.

Kazuri Beads is a five minute drive away. It began in 1977 as a workshop making ceramic beads to give a couple of local women a wage, and now employs several hundred, most of them single mothers. The tour walks you through rolling, firing and hand-painting each bead, and takes about forty minutes. It is a working factory rather than a demonstration, which is what makes it good.

In the afternoon, Bomas of Kenya, back towards the park gate. The grounds hold reconstructed homesteads from a range of Kenyan communities, each built in the appropriate materials and laid out the way it would be, and the large auditorium runs a daily programme of traditional dance and music from around the country. It is unashamedly a showcase rather than a village, and it is also the only place you will see this much of Kenya in one afternoon.

The Nairobi National Museum, founded in 1910 and rebuilt this century, is the best museum in the region and the right way to finish. The human origins gallery is the reason: Kenya's Rift Valley has produced an extraordinary share of the hominin fossil record, and the Leakey family excavated a great deal of it. What is on display, alongside casts, is the sort of thing most countries would keep behind glass in a capital far away.

The rest of the building covers Kenya's birds and mammals, its cultures and its politics, and there is a gallery of Joy Adamson's portraits of people from communities across the country, painted in the 1940s and 50s, which is quietly extraordinary. Outside, a snake park and a botanical garden fill another half hour if the flight is late.

Then the airport. Give yourself two hours for the drive to Jomo Kenyatta if you are leaving in the afternoon, because Mombasa Road at that time of day is exactly what everybody warns you about.