Lisbon is an elegant city of pastel buildings with terracotta roofs, jumbled together on steep cobbled streets. So it was a shock to see a 40-foot burglar bursting out one of them.

I had just arrived and was taking a taxi to the city's enticing Bairro Alto. Looming out of the dark on Av Fontes Pereira de Melo was an enormous building. Where the windows should have been, there was nothing but starry night sky, and an immense black figure making his escape. I got such a fleeting glance as we sped past that I wondered if I had imagined it. Retracing my steps the next morning, I found a cluster of formerly grand, now derelict, buildings. Artists had been let loose on their crumbling walls and boarded-up windows. As well as the six-storey-high "burglar", there was a figure drinking from planet Earth with a straw, a giant crocodile, and some sinister birdlike creatures. The scale was breathtaking, and the gaudy colours incongruous but brilliant in the busy street.

This vast collection of graffiti art turned out to be the work of the Crono Project (cronolisboa.org), which is commissioning artists to transform neglected buildings in the business district instead of abandoning Lisbon's crumbling heritage to the developers. The project began in June last year and is expected to conclude this July with an exhibition. The next artwork will appear between 15 and 22 February.

Street art has long been a part of Lisbon's culture. Until the 18th century, there was a tradition of all-white buildings. After the earthquake of 1755, richer areas began to incorporate colour and tiles into walls and pavements. Early graffiti was perhaps the poor man's equivalent. Following the democratic revolution in 1974, this self-expression increased. Now, tags and scribbles cover the streets.

Graffiti is either the scourge of the city or part of what makes it unique, depending on your viewpoint. Even if you dislike the disfiguring of an ancient capital, it is possible to distinguish between meaningless scrawls and impressive pieces of urban art. The city council has begun to make such a distinction as part of an urban renewal drive, combining (largely futile) clean-up efforts with conciliatory moves: talking to aficionados, making abandoned buildings available to artists, realising that good-quality street art could be an asset. Pedro Soares Neves, a consultant to the council, has seen officials develop an unrivalled enthusiasm for urban art. Contrast with Barcelona, where a draconian crackdown in 2004 caused the disappearance of much graphic and performance art from the streets.

I decided to make graffiti-spotting the purpose of my city break and set off to see what treasures I could unearth. I noticed gems I'd normally miss. Little boutiques around the Rua da Rosa were decorated by graffiti instead of paintings. Galleries had murals painted directly on to their brick walls. Every surface – a billboard, a street sign – seemed to display a face, an animal, or a stencilled message. One slogan that stood out was "Eat the rich", a sign of the economically troubled times. On the climb to the ruined Castelo de São Jorge, which affords fantastic views of the city, the way was pointed by a graffitied monkey.

Near the castle in the Mouraria district, a maze of medieval alleyways, was street art with a difference. Rather than spray-paint, Englsih artist Camilla Watson (camillawatsonphotography.net) uses photography. Tribute is a series of portraits of elderly residents, printed on the walls of the Beco das Farinhas where they live. Her exhibits have proved popular with locals and visitors, and will remain in place indefinitely, funding permitting.

Next I headed to the Galeria de Arte Urbana (gau-lisboa.blogspot.com) on Calçada da Glória, which was set up by the council to give street artists a legal place to operate. Many have taken up the invitation, covering the specially erected boards with fantastical creations – one reminded me of Picasso's Guernica. Others have called for real walls to be authorised for graffiti.

Over in Amoreiras I visited the Hall of Fame, Lisbon's biggest and oldest stretch of mural. Some 90s paintings are still there – practically prehistoric in graffiti terms. But Lisbon's street art is no longer just found on the streets. Like Banksy, many Portuguese graffiti artists have begun to exhibit in galleries.

The Vera Cortês Art Agency (veracortes.com), hidden away near the Praça do Comércio, was hosting an exhibition by Underdogs (under-dogs.net), a collective of some of the country's top street artists. Chief among them is Vhils, aka Alexandre Farto, who began by tagging trains and now, at just 23, is fêted in galleries around the world. He is known for his portraits, which are often created in abandoned buildings from materials he finds there. In the Underdogs exhibition, Vhils chiselled a face out of the plaster itself. To see his work on the street, go to Fábrica Braço de Prata, an old munitions factory in the Marvila district.

Other galleries in Lisbon are also embracing urban art. Some are small, quirky venues such as Yellow Pants (yellowpantsgallery.com), but others are mainstream galleries showing graffiti for the first time. The Berardo Collection (berardocollection.com) in Belém is a major museum of modern art that last year hosted work by Os Gêmeos (The Twins), graffiti artist brothers from Brazil. I hopped on the bus to Belém to view the contemporary Portuguese artwork in the permanent collection, as well as pieces by Picasso, Miro and Warhol. Belém has a host of other sights, from the Jerónimos Monastery and the Tower of Belém to the Antiga Confeitaria de Belém, said to serve the best custard tarts in the city, so it's well worth a visit.

Art appreciation is tiring when you have to explore an entire city. Luckily there are plenty of arty hangouts when you need a break. The Chiado district is a good place to start. We had salad and sandwiches at Mar Adentro (Rua do Alecrim 35), a gay bar by night and one of few places that serves food all day. At night, the Bairro Alto is always lively. We stumbled across Império dos Sentidos (imperiodossentidos.com.pt/) on our first night. It was one of the best places we ate, with a mix of Portuguese and international dishes, and art exhibited on the walls. I shared some black pudding from Guarda and then had the ubiquitous but delicious feijoada (bean stew) with cuttlefish and prawns.

For wine tasting, try Alfaia Garrafeira (garrafeiraalfaia.com; not to be confused with Alfaia Restaurant, its more touristy older brother), a tiny wine bar and shop serving mountain cheese, pata negra (cured ham) and other delicacies. The Bairro Alto has dozens of bars, from traditional drinking dens to the high camp and fashionable, such as Heidi (heidibar.com), a "Swiss concept bar". For cocktails, head to Cinco Lounge (cincolounge.com) in the Príncipe Real. Run by a Brit, it's a bit too smart to be "street", but there is a nice mix of trendy locals and knowledgeable tourists.

After a long weekend in Lisbon, we felt suitably immersed in culture while having explored the city and enjoyed plenty of fresh air. That's the beauty of street art: you can see it without being confined to a gallery. Even a bar crawl can double as an urban art trail ... Just watch out for giant burglars.

Correction: This article was amended on 31 January 2011. The original stated that the artist Camilla Watson was Scottish; she is actually Englsih.

Way to go

• EasyJet (easyjet.com) flies from Luton to Lisbon from £53 return. Owners Direct (ownersdirect.co.uk) has apartments in Lisbon from around £20 a day. Visit stick2target.com for the latest Portuguese street-art initiatives