I have always believed that the best holidays are the ones where you accidentally take a wrong turn and find something brilliant, which is just as well because my sense of direction is absolutely shocking. So when my partner suggested we drive down to a little place called Lojt Strand in South Jutland, Denmark, I was already mentally preparing myself for several unplanned detours. What I had not prepared for was the sat nav deciding that the most direct route to our holiday cottage involved what I can only describe as a field with aspirations of being a road.

We had been driving for hours from Esbjerg, where our flight landed, and I was in that peculiar state of travel delirium where every village name sounds like someone clearing their throat. The Danish countryside was rolling past in that very particular way it does, all flat fields and big skies and the occasional red-roofed farmhouse looking like it had been painted by someone who really understood the concept of hygge. Then the sat nav announced we had arrived, and I looked out at what was definitely a cabbage patch.

"Are you sure?" I asked it, which is pointless because sat navs never admit they are wrong.

Turns out I had punched in the postcode while half-asleep on the plane, missing the last digit entirely. My partner found this hilarious for approximately four minutes, which was how long it took to get properly stuck between two particularly aggressive hedgerows and have to reverse half a mile while being watched by some very judgmental sheep. We eventually found the actual road to Lojt Strand by following a man on a bicycle who looked like he knew where he was going, which is my preferred navigation strategy in foreign countries.

The cottage itself was one of those traditional Danish summer houses, all wood panelling and slightly wonky angles that suggest it has been enjoying the coastal air for several decades. We dumped our bags and immediately did what any sensible person does after a long drive and a small crisis: we went for a wander without any particular plan, which is how the real discoveries began.

Lojt Strand sits on the Little Belt strait, and the beach itself is not one of those dramatic affairs with cliffs and crashing waves. It is quieter, more modest, the sort of place where you find interesting stones rather than crowds. We walked along the shore and within ten minutes had stumbled upon a tiny wooden shelter that someone had built into the dunes, clearly for the purpose of watching the ferries glide between Denmark and Funen. There was no sign, no information board, just a bench and a view and the faint smell of someone's earlier barbecue. We sat there for an hour, watching the light change, and I felt that particular holiday feeling of having accidentally found exactly where you wanted to be.

The next morning, determined to find breakfast supplies, we took another wrong turn trying to locate what we thought was a village shop. Instead we found ourselves on a narrow lane that ended at a small harbour, the kind that barely qualifies as such, just a few boats and a shed selling smoked fish from the morning's catch. The man running it spoke approximately six words of English and I speak approximately zero Danish, but through the universal language of pointing and smiling, we acquired the most extraordinary smoked mackerel I have ever tasted, plus directions to the actual shop which was, predictably, in completely the opposite direction from where we had been heading.

That became the pattern of the week. We set out with vague intentions and found better things by mistake. A supposed shortcut to Aabenraa led us instead to a hidden cove where locals were swimming, the water surprisingly warm in late August, shallow and clear. We joined them, borrowing a spot on the grassy bank where someone had left an old wooden ladder for easy access. No lifeguard, no facilities, just the gentle absurdity of floating in the strait while cargo ships passed in the distance.

One evening, attempting to find a recommended restaurant, we got lost in what I can only describe as a forest of very organised fruit trees, all in neat rows with signs we could not read. A woman walking her dog took pity on us and, through gestures and the word "cider," communicated that we had wandered into a small orchard that sold its produce from a shed on Saturdays. It was Wednesday, unfortunately, but she showed us a path through the trees that emerged onto a lane we recognised, and we found our dinner eventually, though I am fairly certain not the dinner we had originally intended.

The thing about South Jutland, I came to realise, is that it does not shout. It is not Copenhagen, all design and bustle. It is patient, it waits for you to slow down enough to notice it. The landscapes are subtle, the pleasures are small. A good smokehouse you find because you took the scenic route. A swimming spot that exists in local knowledge rather than guidebooks. An orchard that is just there, being an orchard, not particularly bothered whether tourists find it or not.

By the end of the week, I had stopped worrying about getting lost. In fact, I started to rely on it. Our final morning, we set out with no destination at all, just a general heading towards the water, and found a small peninsula where someone had arranged stones into a rough circle, clearly a fire pit for occasional gatherings. We sat in it like children in a makeshift fort and watched the ferries again, smaller now that we understood their rhythm, and I thought about how my terrible sense of direction had become the best thing about the trip.

I still got us lost on the drive back to Esbjerg, naturally. Found a village with a windmill that was not on any map I could find later, stopped for coffee in a place where nobody seemed surprised to see tourists because they barely seemed to see us at all, which was perfect. We made the flight with minutes to spare, slightly breathless, slightly chaotic, already laughing about the panic.

That is the thing about hidden gems, I suppose. You cannot plan for them. You can only make yourself available to being lost, and trust that somewhere between where you meant to go and where you end up, there is something worth finding.