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Why go now?
Winters are chilly but usually dry in this exhilarating city, which is starting to challenge Vienna and Prague as Central Europe's finest. Budapest's thermal baths and pools warm the cockles on even the coldest days, and the city positively blossoms in March, when it stages a world-class Spring Festival: two weeks of classical and contemporary music, dance, theatre and art exhibitions; call 00 36 1 486 33 11 or visit www.festivalcity.hu.
Hungary's national carrier Malev (0870 909 0577; www.flymalev.co.uk) has three flights a day from Heathrow, and two from Gatwick. British Airways (0870 850 9850; www.ba.com) flies daily from Heathrow and Gatwick. EasyJet (0905 821 0905; www.easyjet.com) and Wizzair (0048 22 351 9499; www.wizzair.com) each have two flights a day from Luton, and easyJet also has a daily connection from Gatwick. Ryanair (0871 246 0000; www.ryanair.com) flies from Bristol, East Midlands, Liverpool and Prestwick; Jet2 (0871 226 1737; www.jet2.com) has five flights a week from Manchester; and next month, Aer Lingus (0870 876 5000; www.aerlingus.com) starts a weekly service from Belfast.
Budapest's Ferihegy Airport is 16km from the city centre. You can take a bus to the nearest Metro station and continue into the city for under a pound, or invest 3,900 forints (Ft) – just over £11 – for the return trip by shared minibus. Seats can be booked before arrival (00 36 1 296 8555; www.bud.hu), or from the tourist offices at both airport terminals. A metered taxi costs Ft4,000-Ft6,000 (£11.50-£17), depending on where in the city you're staying.
Get your bearings
The majestic (but rarely blue) Danube is the focal point, dividing the city into two contrasting parts, Buda and Pest, which were administratively separate cities until 1873. Buda, to the west, is hilly, ancient and best for sightseeing; Pest, sprawling away from the east bank, is larger, more commercial, and flat. The city's three Metro lines intersect at Deak Square (1) in Pest, from where the great 19th-century boulevards fan out. The fare is Ft230 (90p), but you can simplify your life – and save money – by buying a Budapest Card, which provides unlimited public transport and reduced or free entry to about 60 museums and sights. A 48-hour pass costs Ft6,500 (£19), valid for one adult and a child of under 14. The 72-hour equivalent costs Ft8,000 (£23). Cards can be bought at hotels, travel agents, museums and tourist offices.
The Hotel Gellert (2), at Szent Gellert Ter 1 (00 36 1 889 5500; www.danubiushotels.com/gellert) on the Buda bank near Liberty Bridge, is a monument to Budapest's Art Nouveau heyday of the early 20th century. There are stately public rooms, ornate balustrades, a Vienna-style coffee shop, and the city's leading spa next door (see 'Icing on the Cake'). Double rooms in winter, with breakfast and complimentary use of the spa, start at €135 (£104) in low season, although you may want to pay an extra €25 (£19) for a view of the Danube. Be aware that some of the rooms and corridors have a Soviet-era grimness about them.
On a corner of a cobbled square in the well-restored Castle District, Hotel Burg (3) at Szentharomsag ter 7-8 (00 36 1 212 0269; www.burghotelbudapest.com) occupies a prime location a few steps from the magnificent Matthias Church – and is comfortable and spacious. Doubles are €99 (£76), including breakfast. The Pest Hotel (4) at Paulay Ede utca 31 (00 36 1 343 1198; www.hotelpest.hu) is an excellent, family-run establishment with 25 rooms in a restored 18th-century building near the Opera House. Ask for a room overlooking the quiet courtyard. Doubles cost €86 (£66), including breakfast.
Take a hike
Wooded pathways wend their way from the foot of Gellert Hill to the summit. As you gain height on the half-hour ascent, the south of Buda and most of Pest opens out before you. One landmark on the hill is the Liberation Monument (5), celebrating Hungary's freedom from the Nazis (but not before the retreating troops had blown up all the bridges on the Danube). Another is a church built inside a cave that was closed down during the Soviet era .
Take a view
...from the forbidding Citadel (6) at the top of Gellert Hill, 140m above the Danube. Built by the Austrian Habsburgs in the 1850s following a failed Hungarian uprising, it's now an entertainment complex, with a hotel, restaurant, nightclub and a permanent exhibition of the city's Second World War defences (open 9am-5pm every day; admission Ft1,200/£3.60).
Lunch on the run
There are superb snacking opportunities in the city's seven covered markets, the largest of which is Nagy Vasarcsarnok, also known as the Central Market Hall (7), across a square at the southern end of Vaci utca. Most of the eateries are on the upper level.
Stock up on the national staples of garlic and paprika at the market, which opens between 7am-6pm on Mondays-Fridays, and 7am-1pm on Saturdays. Budapest has acquired nearly a dozen new shopping malls in recent years, including Westend City Center (8), the largest in central Europe, but prices are similar to those in Western Europe. Besides, the small shops and boutiques further along the attractive pedestrianised section of Vaci utca (9) and its adjoining streets are more engaging and less like those back home. Look out for handmade shoes and beautiful Hungarian porcelain at affordable prices.
The best of Budapest's visual art is to be found in a handsome neoclassical building, built to celebrate Hungary's millennium in 1896. The Museum of Fine Arts (00 36 1 469 7100; www.szepmuveszeti.hu), on the north side of Heroes' Square (10), has an impressive collection of European paintings and drawings from mediaeval to modern times. There is even an English section, featuring Reynolds, Hogarth and Gainsborough. Admission is free, but expect to pay around Ft2,200 (£6) to see the temporary exhibitions that change every three months. Coming soon (21 February) are drawings by French masters, on tour from the Louvre. Open 10am-6pm daily except Monday (to 10pm on Thursday).
Andrassy utca, the fin de siècle boulevard that brings to mind the Champs-Elysées, is the place to be as the sun goes down. Set back from this magisterial avenue, Franz Liszt Square (11) had 22 bars at the last count, not all of them Irish. Nearer the centre, the cellar bar at Bor La Bor (12) (Veres Paine ut 7; 00 36 1 328 0382) is a hubbub of noise, but has some intimate corners, too.
Dining with the Locals
For sheer value, it is hard to improve on the Trofea Grill (13) at Margit Korut 2 (00 36 1 438 9090; www.trofeagrill.eu), an excellent buffet-style restaurant near Margaret Bridge, where the trays of hot and cold meat, fish, vegetables and desserts are constantly replenished. Prices, which include house wines, soft drinks and coffee, vary according to days and mealtimes. From Monday to Thursday evening, the charge is Ft3,999 (£11) per person, rising to Ft4,499 (£13) for the "improved menu" at the weekend.
If the prospect of dinner in Budapest without an accompanying Gypsy band is unthinkable, Arany Barany (14) – next to the British Embassy at Harmincad utca 4 (00 36 1 317 2703; www.aranybaranyetterem.hu) – is as good a mid-range etterem (restaurant) as any. It specialises in lamb dishes at reasonable prices, and a trio of entertaining musicians who periodically succeed in silencing the diners.
Sunday morning: go to church
At the heart of the Castle District, Matthias Church (15) at Szentharomsag ter 2 (00 36 1 355 5657), also known as the Church of Our Lady, has been damaged, destroyed, rebuilt and restored at various phases of its 700-year life. The ornate, neo-Gothic construction we see today dates largely from the late 19th century. The stained-glass windows are glorious, and the 4,500-pipe organ, along with the building's excellent acoustics, make it an excellent venue for classical and choral concerts. Mass is celebrated four times every Sunday morning, at 7am, 8am, 10.30am and noon.
Out to Brunch
Between the wars, the Central Kavelaz (16), at Karolyi Mihaly utca 9 (00 36 1 266 2110; www.centralkavehaz.hu), was the centre of Hungarian intellectual life, occupying part of a publishing house. It closed after the Soviets moved in, but is now thriving again, serving meals, drinks and coffee all day long to what the owners describe as a "tarnished milieu". Aproned waiters scurry between the marble tables and leather armchairs in the café section, where patrons spread out their newspapers and bring their laptops for the free Wi-Fi. There's a formal dining section, but best of all is the open, upper gallery overlooking the throng. All-day brunch (about Ft5,000/£15) has become a Sunday morning institution. Typical of the new Budapest, Central is an all-round delight.
A walk in the park
The city's finest park is gloriously set on Margaret Island (17), in the middle of the Danube, connected to the rest of the city by boat, and by bridges at both extremities. There are wooded walks, ornamental gardens, monastic ruins, and two spa hotels and a bathing complex fed by hot springs. The noise and bustle of downtown Pest is only a short walk away, but you wouldn't know it.
Take a ride
A sightseeing cruise on the Danube is especially rewarding in the evening. Many vessels serve dinner on board, and the great bridges and historic buildings – especially the Parliament building (18), modelled on Westminster – look at their best from the river when darkness falls and the illuminations take over. A 90-minute trip with Hungaria Konzert (reservations 00 36 1 317 2754; www.ticket.info.hu), which is moored behind the Kossuth Museum-Ship (19) on the Pest bank, costs Ft3,300 (£9), rising to Ft7,200 (£20) if you include the buffet dinner.
Icing on the cake
The bountiful underground supply of warm, mineral-rich water, used for both relaxation and medication, makes Budapest one of the world's great spa cities. The best-known of about 40 spas and baths is the Gellert, next to the hotel (2) of the same name: a wonderfully grand and steamy temple full of pillars and statues and mosaics, but with often rather too many visitors. For a more authentic (and less expensive) experience, try the Rudas Baths (20) at Dobrentei ter 9 (00 36 1 356 1322; www. spasbudapest.com). They're Turkish rather than Hungarian baths: designed in the 16th century for the Pasha of Buda, with shafts of light piercing the steam through a magnificent central dome. The mixed sessions are on Friday and Saturday nights (10pm-4am) and on Sundays (8am-5pm). Admission to the baths is Ft2,200Ft (£6).