Off-season, after the summer holiday rush, Dubrovnik’s deep blue Adriatic is peaceful but still warm enough to swim in, and its white pebble beaches edged with pine trees remain inviting.

But the magnificent Unesco-protected Old City offers more than just a beachside break. It is a glamorous base for wine and food lovers with unique experiences on its doorstep, ranging from oyster farm dining to home cooking with local families.

We arrive on a Friday evening to the Hotel Excelsior – a stone’s throw from the Old City walls and a favourite of international jetsetters, including royalty and Game of Thrones stars, for its stunning seaside location.

To the sound of waves directly beneath the floor to ceiling windows, guests begin the evening with cocktails as the sun sets. It’s fine preparation for indulging in a fine-dining extravaganza at the Excelsior’s Sensus restaurant, which pairs local delicacies – such as grilled squid and marinated red mullet – with little-known but superb Croatian wines.

The pedestrianised Old City is so close that there’s time for a late evening stroll through the medieval gates and into its beautifully illuminated palazzi, elegant baroque churches and main streets, lined with busy bars and luxury stores.

But when the sun rises over the glorious rock-and-pebble coast of Lokrum islet (ferries run every 15 minutes from the Old City), it’s time to explore a little further afield.

Croatians are rightly proud of their oysters, which they assure you are the best in the world. We drive about an hour past yet more coves lapped by crystal clear water up to the Pelješac peninsula and Mali Ston Bay, where we are transported by a small boat, out to a floating pontoon set up with stoves and tables.

Our hosts greet us with a welcoming shot of grappa – we are politely informed that it would be rude not to partake, 10.30am or not – before we watch them haul mussels and oysters straight out of the sea. The oysters are opened before us, sprinkled with lemon juice and we all agree they are the most delicious any of us have ever eaten – accompanied by wine from vineyards just a few miles away.

After lunch, sun-drenched and gently sozzled, we then continue on through the gentle hills covered in grape vines towards the family boutique Saints Hills winery. The winery’s owners have fulfilled their wish to present Croatian wines and native varieties that have been made in a modern way “with respect for nature”. Each of the three vineyards, as well as their olive orchard, is named after a saint.

Visitors can while away the afternoon over a five-course tasting menu with wine matching, and we dine on calamari risotto, beef cheek, cheeses and at least two desserts, while adding to the day’s bottle count quite considerably. All ingredients are fresh and local, with vegetables and spices grown in the old stone house’s own garden. Dishes tend to follow Dalmatian traditional recipes made with a little twist from the chef.

We come away with a bottle of the Saints Hills Dingac 2016, a big winner for the vineyard at international competitions for its palate “dominated by plums, dark chocolate, carob, and cookie aromas, followed by smoky scents of tobacco”.

Everywhere we go, family seems to be at the heart of Croatian life. The next day we travel inland for about 45 minutes from the Old City to the lush Konavle Valley and Kameni Dvori, where the Mujo family proudly traces its ancestors back to the early 16th century and currently live as an extended group of 19.

We are welcomed into the family home – with a shot of grappa, of course – and are introduced to matriarch Stane and her daughter-in-law Katarina, who cheerily inform us that we’re cooking our own dinner tonight – bread from scratch, chicken soup with pasta and vegetables, and cake to finish. And wine, obviously… rather a lot of it.

Firstly though, we wander around the family’s extensive garden, picking peppers, tomatoes, herbs and figs grown under the Croatian sun, before we visit the wine shed, where the owners are only too happy to provide an early tasting on their Malvasia, a Konavle indigenous grape variety.

Cooking with the beautiful Stane is a joyous experience. Standing side by side in her kitchen as she shows you how to make the meals handed down from generation to generation, she chatters away and I chatter back, drinking wine in front of the huge kitchen fire for two hours. It only occurs to me as we’re clearing up that neither of us has spoken a word of the other’s language.

Dessert is Padišpanj, a sponge cake known as Bread of Spain, which contains a little flour, 12 eggs and 12 tablespoons of sugar, and tastes as good as it sounds. The cake is traditionally served on special occasions and became an ideal gift for wedding ceremonies. Just when we thought we couldn’t drink any more wine, our hosts present us with the cake’s ideal match – a sweet wine also made from Malvasia grapes.

Our weekend is almost at an end and there is a plan to go out in grand style. Back at the Excelsior, we walk for barely a minute along the cliff to Villa Agave, a private residence of such stunning beauty and exclusivity that Francis Ford Coppola considered it his Dubrovnik home away from home, and Harrison Ford was a recent guest with his family.

The villa is part of the Excelsior, and we end our weekend dining on one of its five stone terraces, attended to by the hotel’s chefs over too many courses to count. It is a feast of local seafood, the freshest local ingredients and more beautiful wine, all as the walls of the Old City are softly illuminated as the sun goes down. A fine return to the joys of travel indeed.