If you're looking at a map, it's hard to know where Antibes ends and Juan-les-Pins begins. These Riviera neighbours are lumped together in brochures, giving the impression that it's all one big cohesive sprawl along the Cap d'Antibes peninsula between Cannes and Nice. It isn't, of course – not when you've got ancient Antibes with its Greek origins and 16th-century ramparts sitting next door to the art deco elegance of beach-lined Juan-les-Pins. They couldn't be more different, nor would you want one without the other.
I wasn't sure which town to stay in last summer, so I tried both. There are surprisingly few hotels in Antibes itself: most are in Juan-les-Pins or tucked away further along the peninsula. Renting a flat, however, is an affordable option. English expatriates Louise and Paul have a couple of studios on the fringes of the old town near the adjoining beaches at Ponteil and Salis. Mine was on the first floor, with the sea right in front. Breakfast was on the balcony, with a view of the ramparts of Vieil Antibes just to the left of the vivid Mediterranean. I could think of worse ways of starting the day.
A three-minute stroll through the stone bastions leads to one of the more evocative Picasso museums. Quite a few towns along the Côte d'Azur lay claim to being a former home of the great man (well, he did get around a bit), but few match the grandeur of Chateau Grimaldi. The imposing 16th-century chateau fell into the artist's hands for a mere six months in 1946, but he left behind a decent number of works in what became the first museum dedicated to the artist. It also houses his La Joie De Vivre, which he painted here. The joy captured in the painting is evident when you walk out into the sculpture-strewn garden and take in the sea view he woke up to every day.
Wander through the maze of narrow streets from the museum and you soon reach the large covered market in Cours Masséna. It's so easy to get carried away by the produce here: olives, cheese, tapenade, fresh fruit and veg, plus the wonderful charcuterie brought in by Corsican traders.
Once the stallholders pack up at 1pm, the restaurants lining the market spread their tables out for lunch. For a surreal aperitif, head downstairs to the Bar Absinthe in the basement of an olive-oil shop just off the market. You can't miss the big green neon sign, although it might look a bit blurry on the way out.
The cave-like interior does a good job in evoking the atmosphere of an early 20th-century drinking den. Vintage posters cover the vaulted ceiling, and rows of glasses are backlit with the distinctive colour of the green fairy, as absinthe is nicknamed. It gets quite raucous in the evenings when they have live music, but on this quiet Sunday afternoon it felt deliciously louche to be knocking back a 68-proof spirit.
Time for a reviving walk through the streets of Vieil Antibes, where the houses seem intent on outdoing each other with their floral displays. Hidden away in a small square is Safranier, an autonomous commune with its own small town hall and a tiny street named after Zorba The Greek author and former resident Nikos Kazantzakis. It's also home to Le Safranier, an unpretentious restaurant serving lovely authentic Provençal dishes to what looked like the owner's large circle of friends. It's the sort of place you'd expect to see in a hilltop village, not the Riviera.
At the top of the town is a gate leading to Port Vauban and Vieux Port, the enormous marinas that separate Antibes from the dramatic 16th-century Fort Carré perched on a rocky outcrop. The marinas with their expensive crafts are about the flashiest sights in Antibes; it's not the place for the vulgar ostentation you see along the Côte d'Azur. It might be a different story in some of the moneyed enclaves along the Cap d'Antibes, however.
I hired a scooter to explore the rocky peninsula of the Cap. As you would expect, there are expensive villas hiding behind iron gates and giant shrubbery, as well as luxury hotels such as the Hotel Cap Eden Roc, favourite haunt of film stars during the Cannes Film Festival. But there are also inviting coves such as the Plage des Ondes, and a museum devoted to Napoleon, who had been incarcerated in Fort Carré.
A winding path takes you uphill to the Phare de la Garoupe, one of the most powerful lighthouses along the Mediterranean coast, and a chapel that marks a centuries-old pilgrimage site. Broad stone benches invite you to take in the views of the peninsula and the mountainous hinterland beyond the coast. Even though it's a popular area for picnickers and walkers, there's a relaxing feeling of peace under the pines. It seemed the moment to tuck into the boar sausage I'd bought from the Corsicans.
Peace is something you won't find a lot of in Juan-les-Pins, but perhaps that's what makes it such a good neighbour for Antibes. Juan-les-Pins buzzes during the summer season, its long beaches and pontoons blazing with the colours of thousands of sun loungers and parasols. It gets noisier every July during Jazz à Juan, which is Europe's oldest jazz festival. But even when music isn't filling the summer air, the streets throng with people eating on the palm-shaded restaurant terraces until the early hours. It's like a civilised version of Ibiza.
Not everyone wants a party, though, and I was happy to enter the tranquil Hotel Sainte-Valérie. This former religious school is a Provençal oasis, elegant in shades of ochre and terracotta, its private garden big enough for cooling palms and a pool. Yet it's less than a 10-minute slow amble back to the seafront.
There's a certain bling you can't escape on the Riviera, but unlike Cannes, this peninsula doesn't feel as if it has sold out to the highest bidder. There's a line attributed to Graham Greene about Antibes being the only town on the Côte d'Azur not to have lost its soul. Whether he said it doesn't really matter; it has the ring of truth.
* Holiday Bikes' (00 33 4 93 61 51 51; holiday-bikes.com) scooter hire from €39 a day.
* HomeAway Holiday Rentals ( holiday-rentals.co.uk) offers two seafront studio flats from €130 per night with a minimum three-night stay; the property code is 83543.
* Hotel Sainte-Valérie, Rue de l'Oratoire, Juan-les-Pins (00 33 4 93 61 07 15; juanlespins.net) has doubles from €180 per night, with breakfast extra at €20.
* Picasso Museum, Chateau Grimaldi (00 33 4 92 90 54 20) is open daily except Monday; times vary according to season, admission €6.
* Bar Absinthe, 25 Bis Cours Masséna (00 33 4 93 34 93 00).