We leave the Amsterdam-bound Eurostar at Rotterdam, just 3½ hours from London, and swap platforms for a 23-minute ride to The Hague. The “city of peace and justice” (who wouldn’t love that?) is home to the Dutch parliament – in the 13th-century gothic Binnenhof – two of the royal family’s three residences, and the international court of justice, housed in the neo-Renaissance Peace Palace. What’s more, several of the Netherlands’ most famous paintings are in the Mauritshuis, the best-known of The Hague’s many art galleries.

It feels as if there can be barely anything left over for Amsterdam, but The Hague has a further asset that for many would trump the rest: miles of wide sandy beach 15 minutes away by (of course) bike, at Scheveningen.

Yet despite – or maybe because of – all this, The Hague doesn’t set its cap at tourists. It feels like a city for locals – and perhaps visiting politicians and lawyers. So we swerve the chain hotels and live for a few days like those fortunate locals, in a stylish duplex conversion on the edge of the 19th-century Statenkwartier neighbourhood, rented via Airbnb. It’s a 10-minute tram ride to the beach and the same to the centre.

The Hague claims to be the greenest city in the Netherlands and plans to be carbon neutral by 2030, ahead of the rest of the country, thanks to solar, wind and hydrogen projects. News of a €50-a-day parking scheme was overegged in UK reports – it applied to very few streets and has since been changed – but there is a notable lack of cars in The Hague. The trams and buses are frequent, cheap and pay-as-you-go by card, but most people, of course, ride bikes. The cycle lane outside our Valeriusstraat pad is well used, especially by families, with knee-high moppets confidently swooshing along beside their parents.

So we join them, on bikes rented from Haagsche Stadsfiets. It’s a joy from the start as cycling is so delightfully normal here: no one’s in Lycra, or wearing a helmet. “For us, cycling means freedom,” says our guide, Remco. “We don’t allow anything to interfere with that, like special clothing or helmet laws.” Old women are riding around in frocks; we see men in blazers and even one in a DJ and bow tie.

We are the only customers at one beachside cafe at 10:30am on a sunny Saturday, and there is almost no one on the acres of pale gold sand. Den Haagers seem to take the weekend at a relaxed pace. Scheveningen was a fishing village in medieval times, though now the old streets of brick terraces are thoroughly gentrified. The only reminder of harsher lives is a statue of a fisherman’s wife, gazing desperately to sea. North-east of here is a stretch of dunes threaded by well-maintained paths, all fringed by sandy beach.

Lungs filled with sea air, we cycle back into town via Westbroek Park and Scheveningen Woods – just two of a claimed 460 green spaces in The Hague. The city’s flag is equal stripes of yellow and green, for beach and parkland. “All 550,000 inhabitants have a tree to hug,” says Remco.

Just south of the woods we come upon the city’s most-photographed building, the splendid Peace Palace. Seat of the international court of justice and the permanent court of arbitration, it manages to be a harmonious mix of Disneyland castle, Byzantine church and London’s St Pancras station, maybe because every nation that supported its building also contributed an element. The doors are from Belgium, marble columns from Italy, a fountain from Denmark, tapestries from Japan. The clock on the main tower is Swiss, there are Persian rugs and the iron railings around its grounds are German. The worst fighting the world has known began shortly after it was finished in 1913, but the intentions were good.

Exploring the city centre by bike is easy too: there are bike racks everywhere, though Remco warns us to always cross tram lines at a 90-degree angle. Every Den Haager has caught a tyre in one at some stage.

The 13th-century Binnenhof, site of parliament and the prime minister’s office, is closed for renovation until 2028, but citizens are not being kept at arm’s length. Platforms in the lake outside are being used for temporary exhibitions, and from a free-to-climb viewing tower at its western end, people can peer over the palace walls at the work in progress and enjoy a 360-degree view of the city.

Anyone who missed last year’s blockbuster Vermeer exhibition in Amsterdam can make up for it at the Mauritshuis gallery. Girl With A Pearl Earring is luminous in the “flesh”, but a bigger surprise is the painter’s View of Delft, with foreground waterside houses in shadow, but sunshine highlighting roofs and towers in the streets behind. I also enjoy a couple of Rembrandts and Fabritius’s storied Goldfinch.

The Hague has canals – Hooigracht and Nieuwe Uitleg are pretty – but a short hop away by train (15 minutes) or characterful tram (30 minutes), Delft, Vermeer’s home, is surrounded by picturesque canals lined with period houses. In this small city almost dwarfed by the huge Delft University of Technology campus to its south (famous alumnus: one MC Escher – see below), there are trips to the factory where the eponymous blue and white porcelain is made, but we prefer wandering little lanes linked by cute bridges, and the main Markt square, with its 400-year-old town hall. Vermeer is buried in the Oude Kerk (“old church”, with leaning tower), while the tower of the Nieuwe Kerk, resting place of Dutch royals, can be climbed for far-reaching views.

Back in The Hague, there are more galleries to visit. Escher in the Palace has hundreds of the artist’s impossible staircases and other optical illusion prints, and the Kunstmuseum is home to masterpieces by Mondrian, Schiele, Kandinsky and Bridget Riley.

Our evenings are spent dining sustainably. The Hague caters well for vegetarians and vegans, be they pizzerias, burger joints or Indonesian specialists.

Our best meal is at Ethica, named after the philosophical treatise by Baruch Spinoza, who spent the latter part of his life in The Hague. Self-taught chef Robin Collard takes green cuisine to another level. The menu is mainly vegetarian, made with produce from his organic garden or sourced locally, but he also serves meat from wild animals that are in surplus in the Netherlands, such as hares and birds that have to be shot for aircraft safety at Schiphol. Even liqueurs and soft drinks are house-made. Importantly, the food is also amazing. Pre-starters of Ukrainian borscht with crispy buckwheat, mushroom jelly with shaved red cabbage, and fresh peas and beans in barbecue sauce leave our bouches very amused. The wild garlic tuile Robin served atop a duck breast starter was pungent, crisp, and unlike anything I’d ever eaten.

For later, there are cosy “brown cafes” to drink in, and any number of live music bars, from the Paardcafe for up and coming talent, to Podium aan Zee by the beach, and rock music stalwart De Zwarte Ruiter.

We don’t see a red light district and aren’t offered any drugs – yet another reason to come here rather than Amsterdam.

• Accommodation was provided by Airbnb. Train travel from London to Rotterdam was provided Eurostar