With its team winning plenty of friends in its debut season in the Premier League, Swansea is flying the flag as a major Welsh tourism destination.

It might seem a long way to travel for a day trip, but nearly 1,500 Norwich fans headed west to Swansea last month to do just that. Of course, the vast majority didn't linger. After a scintillating 90 minutes – capped by a fantastic 3-2 victory for the Canaries – the yellow and green army packed up their scarves and headed back home, by coach, train and car.

Which was a shame, because Swansea – which bills itself as Wales's Waterfront City – has so much more to offer visitors.

And with its team, like our own, adding a breath of fresh air to the Premier League this season – it's the first Welsh club to join the top flight – the city is taking advantage of its heightened profile to fly the flag as a significant Welsh tourism destination.

The clue is in the message in Welsh splashed across the back of the away fans' stand at the Liberty Stadium: 'Croeso' (meaning 'Welcome') – a reminder to visiting supporters that this isn't just any old away day – they're visiting another country.

Of course, to really appreciate the area – marketed as Swansea Bay, Mumbles and Gower – you need more than just a day.

My wife and I took the opportunity of seeing the big match during a long weekend exploring the city and the nearby Gower Peninsula, which was designated Britain's first Area of Outstanding Natural Beauty in 1956.

We travelled from Norwich by train – a trip of around six hours with a change in London – and picked up a hire car for trips out and about.

The city occupies a five-mile sweep of Swansea Bay, ending at the fashionable seaside retreat of Mumbles with its pastel-painted houses, boutiques and Victorian pier.

The importance of the area's railway, port and industries meant that Swansea was hit hard in bombing raids during the second world war. Rebuilding was in typical 1950s style, but now the city is benefiting from some serious regeneration cash.

A boulevard project aims to bring the city closer to the waterfront and make the bay a focus for major events and the marina area has a number of museums and smart restaurants.

Indeed, the Maritime Quarter was the base for our stay, at the four-star Marriott Swansea. With views of the bay and marina, and just a short walk to some of the city's top attractions, it has an enviable position, right next to the prom and beach.

Rooms are stylish, with TV and high-speed internet access, the hotel has an indoor pool and mini gym and the restaurant menu includes international cuisine alongside some tasty Welsh dishes – guests can sidestep more traditional breakfast fare and sample cockles and laverbread for breakfast.

The a la carte menu offers starters such as pan-seared scallops and black pudding in grain mustard cream (�9.50), with main courses including corn-fed chicken supreme, porcini farce, fondant potato and sorrel cream (�16.50). Simply delicious.

On the Saturday, we took a 10-minute stroll through the Maritime Quarter to a museum dedicated to Swansea's most famous literary son.

The Dylan Thomas Centre is housed in the city's old Guildhall which was refurbished in the lead-up to the UK Year of Literature and Writing celebrations in 1995. It now houses the largest collection of Dylan Thomas memorabilia in the world.

The son of an English master at the local grammar school, Thomas lived in the city until his early 20s and worked as a reporter on the local paper. Today, the writer of 'Under Milk Wood' and 'And Death Shall Have No Dominion' is the most quoted writer after Shakespeare – no mean feat for a poet who died when he was just 39.

Perhaps the most poignant exhibit at the centre is the borrowed tweed suit – complete with ink-stained pocket – that he was wearing in the days before his fatal collapse in New York in November 1953. No-one is sure if the ink patch was from Thomas's own pen or that of the suit's owner, the abstract painter Jorge Fick, to whose wardrobe the poet turned when he ran out of clean clothes while staying at the legendary Chelsea Hotel during a lecture tour.

A short walk from the centre brings you to the National Waterfront Museum – the youngest museum in Wales – which focuses on aspects of the country's social and industrial history over the last 300 years. A trip back in time, literally, as running through the museum is a section of track from the first passenger railway that once ran to Mumbles.

After delving into the area's past, one of the best ways of getting an overview of modern Swansea is to take a lift up to the Grape & Olive, on the top floor of the tallest building in Wales.

It's just a short step from the Marriott and serves Mediterranean cuisine in a stylish setting with panoramic views across the city and bay.

You can see across to Mumbles on one side and to the old port on the other, where coal from the valleys came to be shipped to America.

And while taking in the bird's-eye view, diners can feast on signature dishes such as panko crumbed calamari with sticky chilli dressing for starters (�4.25) and fresh egg tagliatelle with scallop and chorizo in tomato ragu (�9.95) for a main course.

Another eaterie well worth a visit is La Parrilla – again within easy walking distance of the Marriott – which offers a contemporary dining experience with a young, lively vibe. Customers make their choice at a display rather like a butcher's counter before having it cooked and delivered to the table.

I plumped for saut� king prawns with a warm salad of radicchio, chorizo and new potatoes with a herb dressing for starters (�7.85), followed by a good-value main course of tenderloin of pork with a date and apple stuffing wrapped in streaky bacon served with brandy cream sauce (�13.50).

The following day we set off to explore beyond the city, on a 40-mile round trip through the Gower Peninsula which took in a lunch stop at Rhossili on the western tip before heading back to Mumbles.

Rhossili is a delight – a giddying, three-mile stretch of unspoilt beach that's popular with surfers, walkers, birdwatchers and hang-glider enthusiasts.

The path down could prove difficult for anyone with walking difficulties but the views are stunning, not least the Worm's Head promontory, shaped like a giant sea serpent, whose name derives from 'wurm', the Viking invaders' word for dragon.

The beach itself is other-worldly – on the day we visited, cattle and horses were browsing the slopes above while a succession of hang gliders surfed the sky before swooping down to the sand.

The timbers of a wreck – the Helvetia which met its end laden with timber in strong winds in 1887 – poke from the beach like the ribs of a dinosaur, its beak-like head studded with nails.

Having what must surely be one of the best views in Britain, The Bay Bistro and Coffee House is perched near the top of the path above the beach. It serves a wide range of food and drinks, from breakfasts to seasonal evening meals, championing local produce including sea bass and mackerel, and is also something of a showcase for local arts and crafts.

There's outside seating and the adjoining Sam's Surf Shack offers lessons from BSA qualified teachers, with equipment available for hire.

On the menu when we visited were a delicious lamb stew and a very flavoursome Greek salad among a host of other dishes.

We ended the day at Mumbles, with a stop-off at Oystermouth Castle. Although it was closed for repairs during our visit, we could still savour its atmospheric presence – the oldest stones date back to the 12th century – looking down on the bay.

For the more active, this area of south Wales has plenty to offer. Afan Forest Park is ranked with California and the Himalayas as one of the world's top mountain biking ranges and, in Swansea itself, The LC is an indoor pool complex, complete with the world's first 'boardrider' indoor surfing experience.

And while you're surfing the waves, this proud corner of Wales continues to ride its own feel-good wave, in the spotlight courtesy of the Swans' Premier League adventures.