It was 5:30 a.m., and I had arranged to join a group of birdwatchers atop a ski jump. The plan had sounded plausible enough when it was proposed over a few drinks the previous evening, but in the cold light of a Stockholm dawn I was beginning to have my doubts. The taxi driver was also skeptical. He knew of the ski jump, but couldn’t believe anyone would ascend it at daybreak to watch birds.

“Impossible,” he said, but agreed to take me just to prove me wrong — we bet the taxi fare on it.

We drove through deserted downtown streets and then, abruptly, entered dense oak forest — the transition from European city to seemingly remote wilderness had taken but seconds. A deer dashed across the road ahead of us.

We reached the disused ski jump, and there, at the top of the tower from which the rusting metal ski ramp sharply descended, was the reassuring sight of a dozen people in bobble hats holding binoculars. The taxi driver conceded the bet and refused even to take a tip; he drove off, shaking his head in wry disbelief.

I climbed the steep tower steps to join my companions. The view was terrific, and we were soon spotting birds on all sides. But something was missing. It took me a while to realize precisely what it was: Stockholm. There we were, comfortably within the limits of a city of 755,000 people, yet looking out at a panorama of green foliage disrupted only by a few seemingly random rooftops, the occasional church steeple and several significant expanses of water speckled with wooded islands. Water and trees, trees and water. And somewhere among it all lay the capital of Sweden.

Later, back on the city streets, I began to realize why it had been so easy to lose sight of this place. Stockholm is determinedly low-rise. Few buildings are much higher than a mature oak tree. The lack of skyscrapers and the abundance of reflective water give the city a bright, airy ambience. Central Stockholm is built on 14 islands, with another 24,000 islands within a short boat ride of the city quays. This marriage of urban and natural environments helps to make this one of the healthiest and most beautiful cities in the world.

The oldest part of the city is Gamla Stan (Old Town), a wonderful, atmospheric jumble of historic houses, quiet squares, ceremonial buildings and beautiful churches connected by a labyrinth of medieval lanes and alleys. You’ll find clusters of the inevitable tacky-souvenir shops here, but I quickly became adept at choosing routes that kept me away from the crowds. Often, as I explored the cobbled backstreets of Gamla Stan, I was accompanied only by the echo of my own footsteps reverberating off ancient walls.

Besides beautiful architecture, Gamla Stan also has plenty of visitor attractions. There’s the Ice Gallery, for instance, which has an exhibition of ice sculptures in a room kept permanently at minus 20 degrees (warm clothing is provided for visitors during summer). Another place worth a visit is the Nobel Museum, dedicated to Alfred Nobel, the inventor of dynamite, in whose name the Nobel Prizes were established in 1901. The museum provides a useful overview of the man and his legacy, and of the recipients of the prestigious prizes.

At the northern tip of Gamla Stan lies the extensive Kungliga Slottet (Royal Palace). This “new” palace was built to replace the “old” palace, which burned down in 1697. A free guided tour of the baroque royal apartments is offered at 1:15 p.m. daily, and is one of the highlights of a trip to Stockholm. Also try to fit in a visit to the impressive Skattkammaren (Royal Treasury), where there is a free tour at 12:15 p.m. every day.

Although Stockholm is easily walkable, I invested in a $68 three-day Stockholm Card (www.stockholmtown.com/stockholmcard), which, as well as providing free admission to 75 attractions, gave me unlimited use of the public transport network. By boat, bus and subway, I crisscrossed the city.

Despite my having Swedish ancestry, my preconceptions of the city had been based on all the usual clichés: the sugary cheerfulness of ABBA; the functional chic of Ikea; the sturdy practicality of Volvos; the Scandinavian angst of Ingmar Bergman movies. All of these elements were present to a degree. But there was much to Stockholm that I didn’t expect. It was cosmopolitan and dynamic. It exuded a strong sense of history and tradition. And somehow it managed to feel simultaneously like a modern capital and a small town.

In the late afternoon, although my legs had not yet shaken off the effects of my dawn ski-jump ascent, I was determined not to miss out on the view of downtown Stockholm from the 347-foot tower of the Stadshuset (City Hall). An antique lift took me up part of the way, and from there I negotiated a succession of rickety staircases and claustrophobically narrow brick passageways to the top.

When I finally broke out into daylight, the view was breathtaking. The entire city was spread before me. To the east lay the tightly packed rooftops of Gamla Stan. To the south, across the width of an expanse of water called Riddarfjärden, loomed the steep cliffs of the island of Södermalm, one of the most recently developed parts of Stockholm. The Hilton Slussen is among the many buildings sitting on those cliffs, offering magnificent panoramas from the guestrooms.

From my vantage atop the Stadshuset, right in the heart of the city, I was amazed to discover that the overriding impression was exactly as it had been at the ski jump. Here I was, with the traffic noise, buildings all around, sightseeing boats sedately plying their routes, and trains constantly coming and going from the Central Station, and yet every vista also contained leafy woodland and vast swaths of water.

The demarcation between city and nature was indistinct. In Stockholm, you can enjoy the best of both worlds.