My first encounter with Eastern Europe's old world is shiny and new: Ferihegy International Airport is Budapest's air terminal. It's modern and clean and there are quite a few friendly Hungarians who speak English reasonably well and can provide travellers with maps, brochures and directions.

Buses and taxis can take you to the heart of the city, but we discover the best way of leaving the new world is on the airport minibus, which offers a hotel drop-off pick-up system and turns out to be reliable and prompt.

The journey from the airport to the centre of this historic city takes you through a mix of housing, industrial estates and then grand hotels, museums and spectacular apartment buildings. Trundling along through tram-lined streets, visitors quickly realise that Budapest's charm lies in its diversity. The buildings are a mix of classical, gothic, and Art Nouveau, but the overall feel is definitely turn of the century.

The capital is made up of two cities - Buda and Pest - with the wide, fast-flowing Danube running between the two. The river isn't blue here, but a muddy brown-grey. Still, it's spectacular because of its size and the magnificent bridges which connect two related, but very different, places.

Western visitors are quickly becoming aware of the grandness and historical significance of the old cities of former communist bloc countries and there is no doubt that Budapest is home to some of the most spectacular buildings in Europe. If architecture is your thing, be sure to mark the enormous, bustling Central Market Building on your list and - at the opposite end of Pest - the colourful Parliament Buildings.

Andrassy Avenue sits within the heart of Pest and dates from the 19th century. Almost two miles long, the avenue was modelled on Parisian boulevards and is home to the cream of eclectic architecture. Here you will find many shops, cafes and museums, as well as Budapest's famous Opera House. Be sure to book a tour, otherwise you will be confined to the foyer and shop.

Also on Andrassy is the House of Terrors, a museum which documents the history of the Nazi presence in Hungary towards the end of the Second World War, and the communist regime during the Cold War. The museum is impressive and a must-see for any visitor to Budapest.

Another reminder of Hungary's communist past is Statue Park on the outskirts of the city. After the fall of communism most of the statues from the era were shipped to this park, and into exile. Hungarians may want to forget, but Statue Park is an increasingly popular stop for tourists. The guide book is worth buying because it gives a sense of history and meaning to the statues.

Pest is home to the best restaurants, bars and cafes in the capital, most of which are located on Raday, in east central Pest, and on some of the smaller streets off Andrassy. Entrees and cakes are delightful and you can find old restaurants and modern bistros side by side offering mouth-watering treats. We recommend the Soul Caf on Raday, which offers a great mix of seafood, vegetarian dishes, creative chicken and turkey fare, in a contemporary, warm atmosphere.

We also discovered a fantastic tea house not far from the Market Building in central Pest. 1000 Teas does literally offer more than 1,000 varieties of leaf tea, and even has more than 100 different green teas on the menu. This cosy place has an Oriental feel and can be found on a small lane off Vaci Utca.

Old charming Buda with its cobbled streets sits on the west side of the Danube, where the plains of eastern Hungary suddenly end and the hills rise in dramatic contrast. The castle and palace sit atop the hill and provide a dramatic view from Pest. You can cross the Danube by bus up to Castle Hill, or take the 19th century funicular (Budavari Siklo) to see the cobbled streets and spectacular buildings which make up this World Heritage site.

Important buildings include Buda Castle, the Fisherman's Bastion and the must-see Royal Palace, which houses the city's main museums and the National Gallery. North of the palace is a medieval residential area with narrow streets and colourful houses and also Ruszwurm, the city's oldest coffee shop.

Hungary is one of the smallest countries in Europe - partly because it lost a significant amount of land under the Treaty of Trianon at the end of the First World War. But Budapest is a large city with more than 70 per cent of the country's two million people. Its spread out too and visitors often make the mistake of trying do all their sightseeing on foot.

Certainly you can't beat walking, particularly on Margaret Island, around Castle Hill, along Andrassy and in Statue Park. But for longer distances use the integrated public transport system which truly is a network. It's inexpensive and covers the city with trams, buses and an underground metro.

If you do happen to wear yourself out walking, you'll be happy to learn that Budapest is a spa city and has more than 80 active thermal springs and wells. The choice of baths and spas is second to none. We spent an afternoon in the city's most popular bathing spot - the Gellert Hotel. This Art Nouveau destination offers mud baths, steam rooms, ultrasound and massage, as well as a swimming pool and hot tubs.

We stayed at the Best Western Grand Hotel Hungaria - with 500 rooms Hungary's largest hotel. It was built in 1915 when it was called the Imperial Hotel and the central block of the building preserves the original facade.

Located on Rakoczi, across from the central railway station, the hotel is on a main traffic route close to the heart of Pest. It's also not far from the Jewish quarter and the magnificent synagogue, the largest in Eastern Europe.

TRAVELFACTS

Sheelagh Caygill flew from Newcastle to Budapest with easyJet. www.easyjet.com or 0905 821 0905. A return fare including tax starts at £40.98.

She was a guest of the Best Western Grand Hotel Hungaria. www.danubiushotels.com