The Rubik's Cube invented by a Hungarian is an appropriate metaphor for Budapest — it's two cities rolled into one, with a myriad facets and colours. And, Budapest's turbulent past makes it an architectural feast — the pot pourri of Roman, Gothic, Byzantine and Communist influences makes walking around Budapest a treat. This city, with a fin-de-siθcle feel, consists of two halves — the opulent hills of green Buda straddling the Danube, and the urban Pest.

At Pest, trams trundle down narrow streets, people spend hours in coffeehouses, and classic buildings attract the eye at every corner. With our guide Andrea Wurmb, we walk on the classy Andrassy Avenue, modelled on the Parisian Champs Elysees — it's a catwalk of international brands and cafes; underneath runs the oldest underground metro system in mainland Europe. At the end of Andrassy Avenue is the magnificent Heroes Square — with its Millennium Monument built in 1896 to commemorate the 1000th anniversary of the Magyar conquest. In the niches of two semi-circles we see the statues of the famous men of Hungarian history — kings, governors and other local heroes.

From here we choose to tour the eclectic neo-Gothic Parliament house with its enormous dome modelled on its British counterpart. The interiors are opulent, laced with gold fittings. We ascend a grand ceremonial staircase with 96 steps (the number being significant as it was the year 896 that the first Hungarians arrived in Europe). The octagonal hall has the dazzling coronation regalia — the crown, the sceptre and the orb. Outside the debating chambers, we see ingenious contraptions — ashtrays which used to allow the members to vote without stubbing out their Havanas. There are numbered slots in the ashtrays — so that the member could vote and resume his smoking! We are pleasantly surprised to see the Prime Minister walk past our group on his way to office. About 300 yards from the Parliament is the poignant memorial to a dark chapter in history — rows of shoes cast in bronze symbolising the killing of Hungarian Jews on the Danube embankment by the Arrow Cross or the Hungarian Fascists in 1944.

Built in 1897 and recently renovated, the Central Market Hall is a great hunting ground for souvenirs. Stalls overflow with Hungarian lace, traditional embroidered waistcoats, hand-crafted porcelain, painted wooden toys and enamelled jewellery. The ground floor is a cacophonous melee of stalls lined with garlands of paprika (the Hungarians use a lot of spices!), salami, sausages, dessert wine and long-necked bottles of the golden Tokaji. Close by is the Latin Quarter or the Raday Utca — a pedestrians-only street, which is a fascinating mixture of Art Nouveau buildings, the Town Hall, cafes, bookshops, souvenir shops and even churches. What's amazing about this city is the way Nature is interwoven with urban life — there's always a park, island, hill or river you can escape to.

We take a bus to the Buda Castle District, a sprawling complex with leafy squares, residential buildings and souvenir shops. Dominating the skyline is the Mathias Church that has endured the Turkish occupation and two wars, and many renovations. Despite the stained glass and the vaulting, the interiors have a mystic Eastern atmosphere. It used to be the scene of coronations; today it is the most popular place where Hungarians get married. A statue of King Stephen on a horse overlooks the Fisherman's Bastion. This looks like a giant sand castle with a series of steps and viewing ramparts for a spectacular panorama of Pest and the Danube. There are seven turrets — one for each of the Hungarian tribes. Andrea takes us to her favourite haunt in the city — Margaret Island. In the Middle Ages, it was called the Island of the Rabbits, and was a hunting preserve; today, it boasts of centuries-old trees, walking paths, electric cars for senior citizens, swimming pools and thermal baths.

What makes this city really special is its spa culture dating back to Roman times. The Turks, who occupied Hungary for over 150 years, brought Ottoman bathing customs here, and today there are over a 100 thermal baths in the city alone. We indulge in some bath-hopping — first on the list is Szechenyl Baths. The bright ochre building looks more like a Baroque palace, with its enormous chandeliers and Baroque sculptures of Venus and Neptune. There are three grand outdoor pools where denizens recharge, socialise, and even play chess on floating chess boards! There are indoor thermal pools, massage centres, and even a restaurant. Stepping out, we cross the Chain Bridge, the oldest bridge on the Danube, to the flamboyant Art Nouveau Gellert Baths with stained glass and a centrepiece atrium. There are pools with freezing cold to really hot thermal water as well as an outdoor wave pool.

For a magnificent finale, we take an evening cruise on the Danube — the river is like molten metal, reflecting the lights of both Buda and Pest with the romantic backdrop of the Castle district, the green Liberty Bridge and the Parliament House.