Descending into Spaccanapoli, two wheels bump along the dark and sticky lava stone. Images, whiffs and sounds rush dream-like in the humid fug: leathery faces, the silvery curl of pesce bandiera, clipped dialect, splashes of sweet and acrid fruit. Nearly three millennia of humanity and molten volcanology make for a vivid Neapolitan experience. Here you have to learn the arte d'arrangiarsi – the "art of arranging yourself" and adapting – and just go with the anarchic flow. On the smoother waterfront cycle path, a vast shimmering panorama opens out across the bay to Vesuvius, Sorrento, Capri.
In 2012, Naples Mayor Luigi de Magistris opened a lungomare liberato (a waterfront "liberated" of traffic) and the experiment continues over this summer. And this weekend Naples hosts the Grande Partenza of the cycling purists' Grand Tour of choice, the Giro d'Italia, for only the second time. (The other was in 1963.) Wiggins, Cavendish and Nibali will be slugging it out for the Maglia Rosa (Pink Jersey) on a scenic 130km circuit that starts on the waterfront, the lungomare of Via Caracciolo.
The sensual curve of Naples' waterfront is the place Neapolitans come to unwind, lick a gelato and survey the azure bay. It's where millions of emigrants set sail for the New World, and was the recent marine playground of America's Cup billionaires. Following a cholera outbreak in 1884, the Risanamento (urban renewal) swept away old fishing communities, fondaci slums and natural beaches, creating a new promenade from Mergellina harbour to Borgo Santa Lucia. Choked by traffic for decades, the lungomare liberato is now a lot less insane.
Inland a few hundred metres along the Riviera di Chiaia, where an older shoreline once lapped Spanish palazzi, I pick up my rugged rental wheels from Luciano Caputo at Napoli Bike. Next door is the mock-Pompeian Villa Pignatelli, built by the Anglo-Neapolitan Acton family.
Over the road, the gravel paths of the Villa Comunale gardens provide an opportunity to test the gears and explore more Neapolitan oddities. The uniformed guards that once kept out barefooted riff-raff are long gone. Everyone passes through the scruffy gardens now – joggers, children and cyclists – to relax amid the Baroque fountains, statuary, Neoclassical buildings and lawns. Only in Naples could the leaking tanks of Europe's oldest aquarium (1872) have serving suggestions for its wriggling organisms. In Norman Lewis's masterpiece Naples '44, the British army sergeant describes General Clark dining on the depleted collection's prized baby manatee amid the wartime chaos. On nearby Viale Dohrn, the Fiera Antiquaria antique market traders present religious artefacts, old postcards and oddball ephemera each weekend morning.
Park gates open on to the prom where the cycle lane hugs the pavement, although this zona pedonale allows room to use the wide road too. From Rotonda Diaz, the Giro sprinters will complete eight lungomare laps and four up and down hilly Posillipo. I join the cycling passeggiata curving around the waterfront towards the Castel dell'Ovo (Castle of the Egg). On this sunny mid-spring Friday afternoon there is a festive atmosphere in 25C heat. Sunbathers stretch out on the breakwater boulders.
A bike-sharing station is planned for Piazza Vittoria, according to Naples daily Il Mattino. From here the Via Partenope restaurants are filling up for lunch. Some are tapping into the waterfront rebirth by offering free use of bikes to patrons. "Eat pizza and ride all you want!" reads one slogan. In the evening this stretch becomes the euro-house pumping movida of the wealthier Neapolitan youth.
Hewn out of Megaride Island, Castel dell'Ovo is on the wedding photo trail. It's built up quite a history and legends since Greeks from Cumae up the coast established the colony Partenope here around 800BC. In his film about Neapolitan music, Passione (2010), American actor-director John Turturro shot a sequence here to accompany the song "Don Raffae" – about a Camorrista taking coffee and dispensing favours from prison. Now the cool interiors host temporary art exhibitions and the towers provide Vesuvian views.
Continuing towards the port there's a mix of Stile Liberty (Italian Art Nouveau) and 20th-century palazzi. Among the fancy hotels with rooftop terraces is Diego Maradona's favourite Royal Continental, and the backdrop to Rossellini's Viaggio in Italia (1954), The Excelsior. A cobbled incline connects the prom to ceremonial Piazza del Plebiscito.
For a detour and taste of the hilly part of the Giro circuit, you can take your bike for free on the Posillipo Funicular from Mergellina Harbour to Via Manzoni, from where it's a couple of miles' ride to the green coolness of Parco Virgiliano with views over the Campi Flegrei caldera and the island of Ischia, where the Giro's stage 2 time trial will take place.
Given the traffic, the heat and my puny calf muscles I forgo the grit of mountain kings and nosedive into a favourite neon-lit chalet restaurant: Ciro a Mergellina. Overlooking the yachts, a genial Eric Morecambe-lookalike waiter glides around with deep-red polpo affogato (octopus cooked in its juices) and huge mozzarella balls.
Mayor De Magistris' attempts to create ZTL (limited-traffic zones) and piste ciclabili (cycle paths) have met anger among many residents and businesses. Inadequate planning, lack of parking and unfinished metro stations have caused protests and strikes. While the lungomare is a success, a Neapolitan farce plays out. The pista to Bagnoli is beset by tunnel traffic and a Riviera palazzo partially collapsed. In Piazza Municipio, the discovery of an ancient port has also held up progress. Controversies about public money, European funds and alleged corruption circle around.
Orazio di Francia of the cycling group Cicloverdi meets me at venerable Caffe Gambrinus. While the dapper baristi maintain the drip and hiss of that essential Neapolitan espresso sugar rush, Orazio lifts his shades and explains that Naples' other obsession with the macchina (car) necessitates a change of culture.
The stats he reveals are startling: Naples has 58 cars to every 100 inhabitants – Barcelona is the nearest major European city with 38, London 31 and Paris 26. There are 4,700 cars per square kilometre; in London it's 1,600 and Berlin 1,150. Poor public transport has throttled the city. For Naples to change, Neapolitans have to change.
Piazza del Plebiscito has been Naples' ceremonial stage for centuries. Instead of La Cuccagna – when despots staged a free-for-all mountainside food fight for impoverished lazzaroni – the square welcomes Knopfler, Springsteen and Giro cyclists this year. Down a few gears, the piazza is the starting point of cycling tours including Pedali nella Notte (Pedals in the Night) each Tuesday and Thursday at 8.30pm. Orazio enthuses about the Cicloverdi (cicloverdi.it) guided day trips all around Campania, from Pompeii and Herculaneum to Salerno and the islands.
From Gambrinus I head up main shopping street Via Toledo (Via Roma to locals). Riders and drivers are in a constant almost-involuntary klaxon conversation. The Neapolitan art of arranging yourself to your advantage is in play. Near Piazza Dante, a family of three on a Vespa hurtles inches from wheels, wing mirrors and pedestrians. A scugnizzo kid on a 200cc pulls an uphill wheelie over potholes. Helmets are not de rigueur.
I make a detour to visit the curvaceous Art Deco Posta Centrale. Italian Fascists built some creepy, inhuman monuments, but this is a beautiful marble-clad Post Office space station. Nearby I pass the graffiti of Ciclofficina Massimo Troisi – the cycling activists' headquarters is named after the late Neapolitan actor and comic genius who pedals, listens and explores Pablo Neruda's poetry in Il Postino (1994).
I tackle the Centro Antico on two wheels. Early mornings, Sundays and the long mid-afternoon lunch breaks (1-5pm) offer some calm. The traffic is limited in this zone but crowds still clog the narrow lanes. Here, stylised traffic-lane logos have faded into the dark stone.
Napoli's Deep History Trip, as one T-shirt puts it, is along Spaccanapoli – literally "split Naples" – and Via dei Tribunali, the main east-west Greco-Roman decumanus forming the ancient street plan grid. I weave through the crowds, over the pocked basalti stones – to get a coffee and sfogliatelle pastry fix at tiny Bar Nilo, beside the shrine to the fallen football hero, Diego Maradona.
After cleaning my palate of the dark cloying arabica – it's common to be served a refreshing glass of water with espresso – I lean against another portly deity. The patched-together parts of the Alexandrian Nile River god statue with bulging cornucopia lounges on a plinth as centuries flow by. Down the darkest end of Via dei Tribunali, Caravaggio's The Seven Works of Mercy at Pio Monte della Misericordia recalls expressions, struggles and charitable acts glimpsed on these dusty streets.
Visitors may love the new lungomare but Neapolitans are divided about the changes. One of the twentysomething staff quips: "We don't need the pista in Naples – we make our own rules."
For Luciano Caputo, "It's a miracle … but extra effort is needed by all Neapolitans to understand which way to go in order to grow … more people need to broaden their horizons." Habits take a little longer to shake off in Naples.
Napoli Bike ( napolibike.com) rents basic bicycles from €10 half day and €15 full day (closed Sundays).
An Artecard ( campaniartecard.it; various from €12) provides museum entry and access to public transport.
May of the Monuments runs from today until 2 June and has free events and tours of more than 200 sights.
Piazza Bellini ( hotelpiazzabellini.it) has functional doubles from €80. Elegant Palazzo Decumani ( palazzodecumani.com) from €100. Arty hotel Micalò (micalo.it) starts at €140. For belle époque style, splash out at the Excelsior ( excelsior.it), from €290 double.