"Anyone here who's been mugged recently?" calls Blinky from the stage, looking cool in his tweed flat cap. Whoooh, the crowd roars, lapping up Nairobi's next big thing, an eight-piece called Just A Band.

"Who's had their mobile stolen?" Woo-hoo! They know what it feels like. I don't yet, and I tap my pockets. He lowers his voice: "We just had our equipment swiped on our way from band practice." Then, his voice rising, he says: "Don't these guys know that Africa is the future?" The crowd erupts again, and the band launches into its flagship dance single, Usinibore. "Don't tell me what I can and can't do/I can cha-a-a-ange the world." It's an optimism Nairobi hasn't felt in years.

Despite the curse of Nairobbery, the city has had a thorough clean-up, but still too many visitors head straight to their eco-lodges on the Masai Mara rather than staying to sample the capital's delights. And few of them know that Nairobi is the centre of a rich music scene.

Just A Band is one of the many new outfits making waves on the Kenyan circuit, having just launched their second album '82 (the year they were born), with a gig at the GoDown Arts Centre, a converted warehouse and exhibition space in Nairobi's hip eastern Industrial Area. A group of geeky young graphic designers, Just A Band are renowned for their award-winning animated music videos. They perform a strange but compelling blend of electronica, funk, hip-hop, and disco, a cocktail they've nicknamed "Afro Electro-gravy". They are a middle-class Kenyan phenomenon, hot on the marketing potential of the internet.

"How did you hear about them?" I ask my sweaty neighbour. "Facebook," she shouts over the din.

I hadn't expected the music in Nairobi to be so varied and vibrant. Weaned for years on Andy Kershaw's BBC Radio 3 slot, with its frequent doses of Congolese rumba and Zimbabwean jit, I expected a scene dominated by benga, with its popping, pulsating bass and aching vocal interweaves. Meaning "something beautiful" in Luo, benga has been the east African guitar music sound since a band called Shirati Jazz took Kenya by storm in the 60s, and it's impossible not to love. But over the past decade there has been a musical and technological revolution – accelerated since president Daniel arap Moi departed in 2002 after 24 years in office – and a chaotic splash of new sounds. On top of the standard soukous (rumba) and benga that you still hear, Nairobi now boasts live fusions of Afro-beat, electronica, R&B and hip-hop, and some remarkably palatable jazz. If you know where to go.

James Murua, of online magazine Nairobi Living, is inspired by the renaissance: "In the 90s the biggest career move was flying to the US. But now we have a ton of radio stations. It's a chaotic, vibrant time. Everyone's writing music."

Being the economic hub of east Africa, Nairobi has drawn musicians from all over the region for decades. Added to the heady mix of local bands singing in their own languages – Luo, Kikuyu, Luhya, Kamba – many Tanzanian musicians have carved a niche in Nairobi, and Zaireans have arrived with their seductive soukous and hip-shaking cavacha.

The big issues now are the twin evils of corruption and tribalism, which led to horrific post-election violence in 2008. And musicians aren't scared of singing about them. Since Eric Wainaina released Nchi ya Kitu Kidogo (Country of Bribes) in 2001, he has inspired hundreds of artists to express hope for a better future, in English, Swahili, and Sheng – the ever mutating Swahili-based street slang, designed to stay one step ahead of the authorities.

Like any big city, Nairobi has plenty of low-quality gigs, but equipped with some online dailies, such as Kenyabuzz.com and Nation.co.ke, you can strike out. Make it your mission to catch Orchestra Super Mazembe and the Harmoniq's Jazz Band.

Every weekend, Nairobians flood into Westlands, the city's drinking district. The writhing floor of Black Diamond on Mpaka Road offers a dim but unhealthy recollection of university nightspots, only sweatier and louder. Gipsy on Woodvale Grove is fun, though the sheer overload of expats and conflicting boomboxes (four) leaves you feeling fragile and bewildered.

But the Klub House, a thumping, jumping, local bar on the Ojijo road, was exactly what I was looking for. Less self-conscious than the GoDown Arts Centre, it had an unchained buzz. Crammed round small wooden tables, people chattered, while waitresses twirled through the close-packed crowd. This was where I found Gogo Simo, one of Nairobi's hottest acts, led by married couple James Jozee and Susan Wanjiru from Mombasa, who brought a raw, good-time energy to the venue. With clear soul and funk influences, they also draw on benga and soukous (of course), zouk – a Caribbean carnival vibe, and chakacha – a bopping dance sound from the coast. Susan was remarkably dynamic, one minute belting like a Swahili Aretha, before descending minutes later into a sizzling near-whisper. I caught the band after the gig, and they explained the inspiration behind their music. Gogo Simo shared the same "you can make it" mentality I found with Just A Band, a reaction to the national apathy brought on by the country's politicians. "That's what our song Kilele is about," said Susan, husky after the performance. "It means the peak, how nothing in life comes easily, but everything's possible if you strive for it, even if the politicians try to get in your way."

I had another gig to catch. I drained my Tusker Malt and taxied to the other side of town, past the grey business district, to the jacaranda-lined avenues of Karen (after Karen Blixen, author of Out of Africa). Taxis are easy to find in Nairobi and generally safe, but they're not cheap. A tenner down, I arrived at a modest-looking entrance to one of the city's most relaxed nightspots.

Talisman on Ngong Road is a loungey, woody restaurant and bar, where sun-beaten blondes sipped gin and tonics and well-to-do young Kenyans basked on low-slung sofas. Here I discovered Maia von Lekow, a twenty-something Kenyan artist, the daughter of Tanzanian jazz groover Sal Davis. A quarter Arab, a quarter Luo, and half European, Maia fuses her musical influences like a lounge chameleon. She sings in English and Swahili. "Bit of a difficult audience," she confided to me on a break. Barefoot, she soon roused them with a rendition of Peggy Lee's Fever. To Maia, the biggest problem is the lack of instruments. "Everyone's trying to write something, but it's running so fast. There are so many drummers, but no drums."

Maia, who lived for years in Australia and Ireland, performed in February's Sauti Za Busara festival in Zanzibar and on 4 July is set to play at Blankets and Wine – a once-a-month event in north-west Nairobi.

So whether its's Blankets and Wine you discover, the trendy GoDown, or the spontaneous Sunday street acts franctically in need of drum kits, keep an eye out for a generation of musicians as they blaze a trail through the night spots and Facebook pages of Kenya's Wild West.

• Opening in Westlands in August, and promising luxury with an authentic flavour of Africa, is the Sankara Nairobi (+254 20 249 0210; doubles from £190). A cheaper option, again in Westlands, and rated highly for its friendliness and charm, is Miti Mingi Guest House (+254 20 444 8585; doubles from £60), off Rhapta Road. Virgin Atlantic flies from Heathrow to Nairobi from £533 return

Daniel Metcalfe is the author of Out of Steppe: The Lost Peoples of Central Asia (Hutchinson, 2009), which has been shortlisted for this year's Dolman travel book of the year