Nearer to Vienna than Dubrovnik, Croatia's pocket-sized capital is closer in character to Central Europe than Eastern Europe. Expanded under the Habsburgs, with pretty parks and elegant façades, Zagreb had been an ecclesiastical and political hub from medieval times. With capital-city status gained after independence in the 1990s, Zagreb is now surprised to find that it has become a tourist destination. They in turn are surprised to find a slightly shabby Central European city rapidly trying to gentrify itself - and, having assumed that it was on the Adriatic, no sea.

Sixteen tram routes pass through Jelačića, where you might start your day pondering a map over a slow coffee. Two walking tours of the city, one north to Gradec and Kaptol, the other south around the Lower Town, become apparent. Each takes about 90 minutes. You might finish one in time for gablec, the local version of elevenses (look out for café signs saying gableci), before completing the next one by lunchtime. Next to Jelaičića on the map but a short, steep climb away are the well-stocked and always busy daily market, Dolac, and the must-see cathedral (Kaptol 31, +14814727, 10am-5pm Mon-Sat; 1-5pm Sun). Further over on Gradac, the other side of Bloody Bridge, is a cluster of sights around the main one of St Mark's Church. This group of churches and galleries is best accessed from a funicular (Tomićeva, every 10mins, 6.30am-9pm daily, 3kn) by Ilica, a gentrifying commercial street running west from Jelaičića. The short ride takes you to the Lotršćak Tower (Strossmayerovo šetalište 9, +14851768, 11am-8pm Tue-Sun, 10kn), a lookout tower built in the 13th century.

Leafy Strossmayerovo šetalište runs by the tower giving a lovely view of the rooftops. And near the tower stands St Catherine's Church (Katarinski trg, +14851950, 10am-1pm daily), built by the Jesuits in the 17th century, with a beautiful baroque interior of pink-and-white stucco. Three main galleries are clustered around it: the Croatian Museum of Naive Art (Ćirilometodska ulica 3, +14851911, www.hmnu.org, 10am-6pm Tue-Fri; 10am-1pm Sat, Sun, 10kn), Klovičevi Dvori (Jezuitski trg 4, +14851926, www.galerijaklovic.hr, 11am-7pm Tue-Sun, 20kn) and the Museum of Contemporary Art (Katarinin trg 2, +14851808, www.mdc.hr/msu, 11am-7pm Tue-Sat; 10am-1pm Sun, 15kn). Just north of Klovićevi Dvori stands the Stone Gate (Kamenita Vrata), the only remaining medieval entrance to the Upper Town. Passing through it, you wander around the cobbled streets of Gradec, looking into little squares, perhaps popping into the Croatian History Museum (Matoševa 9, +14851900, www.hismus.hr, 10am-5pm Mon-Fri, 10am-1pm Sat, Sun, 10kn), a lovely baroque mansion with a collection of photographs, furniture, paintings and weapons thematically relating to Croatia's development.

At the heart of Gradec stands St Mark's Church (Trg sv Marka 5, +14851611, 9am-noon, 5-5.45pm daily); a modest square considering it houses the Croatian Parliament and the Ban's Palace. North, edging towards the verdant slopes of Mount Medvednica, are the Meštrovič Atelijer (Demetrova 1, +14851700, www.hpm.hr, 10am-5pm Tue-Fri, 10am-1pm Sat, Sun, 20kn), a natural history museum and the Zagreb City Museum (Opatička ulica 20, +14851361,www.mdc.hr/mgz, 10am-6pm Tue-Fri; 10am-1pm Sat, Sun, 20kn).

Walking back through the Stone Gate, you come into Radičeva and, crossing back over Bloody Bridge, to one of the most atmospheric and lively streets in Zagreb, Tkalčičeva. Pastel-shaded low-rise old houses accommodate galleries, bars and boutiques.

Crossing the indoor and outdoor markets, your eyes are drawn towards the spires of the cathedral, surrounded on three sides by the ivy walls of the Archbishop's Palace. Around it runs Vlaška, which brings you up to the park of Ribnjak, pleasant by day, filled with amorous teenagers after dark at weekends.

The Lower Town begins at Jelaičića. A criss-cross of streets begins with a pedestrianised zone around Preradovičeva flower market, by the new bar quarter of Gajeva, Preradovićeva and Margaretska. Stern, grey Habsburg façades run down to the station, some with shopfronts unchanged since 1965. Parallel to them are two neatly planned rectangles of green public space stretching north-south as far as the train station, bookended by the Botanical Gardens. This is the so-called Horseshoe, an attempt by 19th-century urban designer Milan Lenuci to create a city in the Austrian mode. Each park is parcelled up into three parts, centrepieced by grandiose landmark buildings of prominent institutions: the Academy of Arts and Sciences, the National Theatre, and the Mimara Museum alongside. Zrinjevac, the northernmost section, features tree-lined paths, a gazebo and a fountain designed by Herman Bollé, responsible for many of Zagreb's major architectural works, including the cathedral. Linked to Jelaičića by Masarykova, the former café-lined hub of the underground music scene, Trg Maršala Tita is notable not only for the neo-baroque Croatian National Theatre but also for the fact that the square has kept its name, Tito. In front of the theatre stands one of the most famous works by sculptor Ivan Meštrović, The Well of Life.

The Lower Town ends at the railtracks and another fin-de-siècle façade, the neo-classical train station, Glavni kolodvor. A major stop on the Orient Express, it echoes another era, when arrival by train was the norm. Next to it was built one of Europe's great railway hotels, the Esplanade, now surrounded by a pedestrianised square of fountains and an underground shopping mall. The main rail lines still run to Vienna and Budapest - only in 2005 was a fast service introduced to Split. South and west run a right-angle of broad avenues: Savska, with its burgeoning business quarter; and Vukovarska, where Orson Welles shot part of his film version of Kafka's The Trial in 1962.

The Lower Town begins at Jelaičića. A criss-cross of streets begins with a pedestrianised zone around Preradovičeva flower market, by the new bar quarter of Gajeva, Preradovićeva and Margaretska. Stern, grey Habsburg façades run down to the station, some with shopfronts unchanged since 1965. Parallel to them are two neatly planned rectangles of green public space stretching north-south as far as the train station, bookended by the Botanical Gardens. This is the so-called Horseshoe, an attempt by 19th-century urban designer Milan Lenuci to create a city in the Austrian mode. Each park is parcelled up into three parts, centrepieced by grandiose landmark buildings of prominent institutions: the Academy of Arts and Sciences, the National Theatre, and the Mimara Museum alongside. Zrinjevac, the northernmost section, features tree-lined paths, a gazebo and a fountain designed by Herman Bollé, responsible for many of Zagreb's major architectural works, including the cathedral. Linked to Jelaičića by Masarykova, the former café-lined hub of the underground music scene, Trg Maršala Tita is notable not only for the neo-baroque Croatian National Theatre but also for the fact that the square has kept its name, Tito. In front of the theatre stands one of the most famous works by sculptor Ivan Meštrović, The Well of Life.

The Lower Town ends at the railtracks and another fin-de-siècle façade, the neo-classical train station, Glavni kolodvor. A major stop on the Orient Express, it echoes another era, when arrival by train was the norm. Next to it was built one of Europe's great railway hotels, the Esplanade, now surrounded by a pedestrianised square of fountains and an underground shopping mall. The main rail lines still run to Vienna and Budapest - only in 2005 was a fast service introduced to Split. South and west run a right-angle of broad avenues: Savska, with its burgeoning business quarter; and Vukovarska, where Orson Welles shot part of his film version of Kafka's The Trial in 1962.