With its steep streets and cobbles, Lisbon is not for the kitten-heeled.

But it is a city of great style and verve, and there are plenty of ways to experience it that are easy on the feet.

The first must is a tram ride. Lisbon’s cute yellow trams have been zipping along its narrow streets, tilting around acute corners and leaving washing fluttering in their wake since 1901. Five routes rattle thrillingly through the central districts. For e1 you can take the number 28 from Graca, on the highest of Lisbon’s seven hills, through the ancient working-class district of Alfama, which survived the earthquake and subsequent fire and tsunami that devastated Lisbon in 1755, and Baixa, a grid of streets leading back from the River Tagus, lined with tiny fashion shops, old brushmakers and haberdashery stores, bars and cafes.

Graca offers a celebrated look-out point, but we made for the castle of Sio Jorge nearby. The castle was once in the centre of the old walled city, ruled by the Moors for four centuries until 1147. Now it’s a peaceful place to hang out, have a coffee and take in the view.

The 28 passes another look-out point, the Miradouro de Santa Luzia, which faces the river over the red roofs of Alfama, whose tiny winding streets are punctuated with fountains that once provided water (separately) for slaves, horses, the people and the king. The tiled wall of the belvedere here depicts the central square or Praca do Comercio and the King’s Palace before the earthquake. Everywhere in Lisbon plain buildings are made glorious with patterned tiles known as azulejos in yellow, green, blue, pink and white. We were warned not to buy any in the weekend flea markets, as they may have been taken from historic buildings.

Next we tried the more expensive tourist option: the Circuito Colina, or hills tour, on a red tram which follows the route of the 28 in a 90-minute ride with recorded commentary. Though we hit one or two tram-jams, the journey was just as clatteringly fast, with several near-misses. We slid from side to side on the basketwork seats, holding on to the shiny brass and wood windows as we attempted to absorb the long history of Lisbon, which goes back to the Romans. Flashing past, I saw a bus shelter encircled by a flourishing grape vine and a pharmacy in Barrio Alto with a huge bunch of herbs hanging at its door.

Back at the waterfront Praca do Comercio, home to the helpful tourist information centre, we abandoned history for a delicious lunch at the swish and super-modern Terreiro do Paco, before exploiting the shopping opportunities of the Baixa. But history soon reasserted itself in, of all places, HM. The fashion shop has a glass floor through which you can see the remains of the stone tanks in which the Romans stored salt fish, still a Portuguese favourite as bacalhau.

The river is so wide in Lisbon that it’s difficult to remember you are not on the sea. The two bridges that span the Tagus seem to stretch almost to infinity; the newer Vasco da Gama bridge is 17 kilometres long. The older bridge, Ponte 25 de Abril, is named after Portugal’s national day, still celebrated with dancing in the streets and the exchange of red carnations, which commemorates the overthrow of the dictator Salazar in 1974.

Sip a cherry gin at the sliver of a bar between Praca Dom Pedro IV and the church of Sio Domingos before taking a look inside the church where the stone pillars are fantastically scuplted into nightmare columns following a fire a couple of decades ago.

While we were in the Rossio district we admired the curving art nouveau doorways of Rossio station (closed for restoration), the fabulous art deco Eden building (once a cinema, now a hotel with a rooftop swimming pool), and the Elevador de Santa Justa, Lisbon’s answer to the Eiffel Tower. This rectangular basket of metalwork lifts people up to the Praca do Carmo in the Barrio Alto district. Here the achingly hip rubs shoulders with traditional coffee and sweet shops. People gather in cafes such as A Brasileira, where Portugal’s greatest poet Fernando Pessoa became such a fixture that a brass statue of him sits outside.

After raiding Bagatela, Lisbon’s stylish answer to the pound shop, where everything is e1.70, we descended to Belem, the waterfront from which Portugal’s great explorers sailed in the Age of Discoveries. The 16th-century Torre de Belem, once a defensive post, is now an icon of Lisbon, surrounded by water. Its white stone architecture is echoed in the Mosteiro de Jer“nimos nearby. The cloister and its church of the navigators, where exotic animals and plants swirl together with angels and monsters in the stonework, are beautiful enough to make you gasp.

Then it was time to squeeze in a pastry, at the Antiga Confeitaria de Belem, where five generations of the same family have served up the warm custard tarts whose taste is the essence of Portugal, and think about the evening: would it be fado, the traditional songs of sorrow, in a bar in Chiado, a district named after a 16th-century poet, or something more contemporary in the same area or in the new Docas entertainment district on the waterfront? We’d saved our feet for some late-night fun.

More information: www.visitlisboa.comFor information about the Lisboa Card, which offers discounts on transport and city attractions, see www.askmelisboa.comTAP flies to Lisbon from Heathrow and Gatwick. Return flights from pound;100 (including taxes). Information and reservations: 0845 601 0932; www.tap-airportugal.co.uk. Lisbon Directions from Rough Guides is a good pocket-sized guide with e-book CD (pound;6.99, www.roughguides.com)