I’m on a narrowboat in Leiden, nursing a filthy hangover, watching this antique city floating past, when I’m awoken from my daydream by a strange whirring noise above me. The glass roof of the canal boat is rapidly descending, and the jolly Dutchman at the tiller is telling me to mind my head. I end up flat on my back, with the roof a few feet above. ‘We have some low bridges here in Leiden,’ says the tillerman, by way of explanation, as if this weird contraption was the most natural thing in the world.

For me, this canal boat with its collapsing roof encapsulates the quirky appeal of Leiden, and why I was so keen to come back here. It’s eccentric but entirely practical, a logical solution to a common problem – and though it seems like a daft idea, it works like a dream. A canal tour is the best way to see this quaint, beguiling city – even if you have to see a good deal of it lying down.

Nobody in Britain seems to have a bad word to say about the Dutch, and whenever I return to Holland I remember why. Everyone I meet here seems so cheerful and contented. Naturally, I’m well aware that this is a dreadful generalisation. I’m sure there must be lots of miserable malcontents in the Netherlands, but I never seem to meet them. Even people doing the most mundane jobs seem bizarrely happy, and supernaturally keen to please. Remarkably, the Dutch combine two attributes which I always used to think were mutually exclusive – they’re both efficient and laid back.

And of course they all speak perfect English – rather better than most Englishmen, in fact. My pathetic attempts to utter a few courtesies in kindergarten Dutch are always met with polite praise – the sort of praise a kindly teacher might bestow upon a diligent but exceptionally stupid child. If anyone else did it, it would seem terribly patronising, but somehow the Dutch get away with it. They know we’re crap at languages, and they don’t care.

Amsterdam was the first place in the Netherlands I ever visited, and for a long time it was the only place. I suspect this makes me fairly typical. I know loads of people who’ve been to Amsterdam and nowhere else in the country. They don’t know what they’re missing. I love Amsterdam but, like a lot of capitals, it’s hardly typical of the country. To get to know the Netherlands, you have to venture further afield, and Leiden is a great place to start.

Getting here is easy. British Airways fly to Amsterdam from Heathrow, Gatwick and London City. You’re in the air for under an hour. Starting prices from all three airports are under £100 return. Amsterdam’s Schipol airport is barely 15 minutes by train from Leiden – about the same time that it takes to get a train from Schipol to downtown Amsterdam.

Arriving in Leiden by train, first impressions aren’t too flattering. The station is on the edge of town, surrounded by bland modern buildings, but the Old Town is only a short walk away, and when you get there you can see why it’s widely (and quite rightly) regarded as the Netherlands’ hidden gem. Only Amsterdam has more buildings from the so-called Golden Age – that heady hundred years or so from the end of the 16th Century to the end of the 17th Century, when the country led the world in virtually every field of human enterprise. While Amsterdam is now a modern metropolis, full of the usual international chain stores, Leiden still has a foot in the century that made its name.

Leiden’s glory days began in 1575 with the founding of Leiden University – the oldest university in the Netherlands. It quickly became one of Europe’s leading universities, a reputation it maintains today. The Oxbridge of the Netherlands, its faculty buildings are scattered around the city, filling its bars and cafes with students and giving its cobbled streets a youthful air.

Leiden University has spawned 13 Nobel laureates, but its most famous student only spent a year there – probably attracted by the duty free wine and beer. Rembrandt was born in Leiden in 1606, the fifth son of a local miller, and went to Leiden University when he was just fourteen. He left after a year to become an apprentice to Leiden’s leading painter, Jacob van Swanenburgh. He spent the next seven years in Leiden, honing his craft, before moving to Amsterdam. It’s an amusing irony that during those seven years Rembrandt was overshadowed by his friend and colleague Jan Lievens, a painter who’s virtually unknown outside academic circles nowadays.

Another amusing irony is the lack of Rembrandt landmarks in his hometown. That his birthplace is no longer there isn’t so surprising. What’s remarkable is that it was torn down in 1929, long after he’d become a household name. You can visit his father’s windmill, and the studio he shared with Lievens, but both these buildings are replicas. Never mind. Rembrandt’s soul doesn’t reside in Leiden, any more than Shakespeare’s soul resides in Stratford. At least his old school, where he learnt to draw, is still there.

By the time Rembrandt left for Amsterdam, in 1628, Leiden’s best days were behind it. The linen trade went into recession, and a religious quarrel between Calvinists and Remonstrants split the city into two rival camps. Yet while Amsterdam became a boom town, Leiden was preserved by poverty. Having quadrupled within a generation, after the founding of the university, its population declined. There were fewer people living here at the start of the 20th Century than at the end of the 17th Century. The Industrial Revolution largely passed Leiden by and so a great many of its historic buildings have survived. De Waag, an ornate trading house built when Rembrandt was still alive, is now a lively restaurant. The old botanical gardens are a relic of Leiden’s leading role in the Age of Reason.

But Leiden isn’t somewhere for sightseeing – it’s somewhere for wandering around in, doing nothing. It’s a place you’re happy to get lost in. The city is so compact, you’re bound to end up where you started off from, eventually. It’s a working city, not a theme park, but it still feels connected to its past. You feel far closer to the Golden Age here than you do in Amsterdam.

Walking back to the station, to catch the train back to Schipol, I wondered what it might be like to live here. Everyone looks so fit and healthy. Everyone seems so chilled out. Yes, I’m sure it’s just an illusion. Yes, I’m sure that if I bought a house here and got a job here and sent my kids to school here, I’d be beset by all the same strains and stresses that I’m beset by back in Blighty. At least, that’s what I tell myself. But deep down, I’m not so sure.

For information about Leiden and the Netherlands, visit www.holland.com or www.visitleiden.nl. Prized Possessions – Dutch Masterpieces from National Trust Houses is at the Holbourne Museum, Bath, from May 25 to September 16