No matter how familiar you become with New York's daedal subway system or its hip Village eateries, the city will never run out of new things to show you. I guess that's almost a truism of life here, but it took me many months of residence to grasp that this place may be one of the world's last great undiscovered territories. When you happen on -- or follow a tip to -- some rarely mentioned, relatively quiet spot in the metropolis, the ensuing sense of satisfaction must be similar to what frontier explorers felt. It is the slightly secretive thrill of revelation.

You do occasionally get tipped off about interesting corners of the city, and in other cases your instinct leads you. This spring, with a friend visiting from out of town, I embarked on a 'mystery tour' partly premeditated, partly improvised.

We began in my own beloved neighborhood of Astoria, Queens, fortifying ourselves for the journey at the Plaza Cafe Lounge on 30th Avenue and 29th Street (near the 30th Ave. stop on the N and W lines). I had been here only once before, on one of the most bitter cold nights of the winter. As the weather improved, its sidewalk seating made me want to enjoy a cool drink in the sun (let me add: lively sidewalk cafes are common in Astoria and a big part of its charm). We had mojitos -- $9 of heaven in a glass goblet the size of a fish bowl. They add about a half-cup of fruit (strawberries, blueberries, watermelon, etc ... your choice) and grind up the mint leaves so the whole thing looks like a specimen of pond water and tastes as delicious as springtime itself.

This had gone well. I felt emboldened to indulge another hankering and see where it might take us. But first we stopped by one of my favorite local haunts, Socrates Sculpture Park, to check out the opening of its summer exhibition.

Twenty years ago, artist Mark di Suvero spearheaded a project to clean up a dumping site on the banks of the East River. Today it's a gallery unlike most you're likely to encounter. Two exhibitions a year see sculptors creating their often whimsical pieces on premises, and the place retains an engaging, higgeldy piggeldy character recalling its junkyard past. On any pleasant weekend or evening of the year, the park is alive with families, picnickers and dog walkers, and in the summer it hosts a range of free events -- film screenings, yoga and capoeira classes, workshops for kids. Separately, but adjacent to the park in Hallet's Cove, the Long Island City Boathouse sponsors free kayaking on summer Sunday afternoons. Unfortunately, we were one week too early for that.

The time had come to venture into Manhattan -- sort of. Roosevelt Island is technically part of that borough, but is located in between it and Queens, in the middle of the East River. I thought of going because the I considered the Roosevelt Island Tram -- for many a means of commuting -- a handy form of free entertainment.

It's an aerial tram, or cable car (I like 'elevated gondola' - the Roosevelt Island Operating Corp.'s romantic term), that runs out to the island from 59th Street and 2nd Avenue in Manhattan. In 2006, it was shut for several months after it stopped mid-journey, stranding passengers for hours. Looking down from its height onto the 59th Street Bridge and river water far below, I imagined how embarrassingly I would panic in an emergency. The car glides easily and the views north and south are a treat, but any unplanned halt and I would convince myself the cables above were slowly tearing.

Roosevelt Island itself is a strange, and strangely beguiling, little place. It's like a small town in the middle of the city, with a population of about 10,000. But since it was developed more or less at once, and within the last 30 years or so, its Main Street has a rather creepy, '70s, insta-town vibe -- a lot of cement in its shop fronts, and a lot of weirdly generic signs saying things like, 'Pharmacy' ... 'Dry Cleaners.'

Nonetheless, we liked it: it's quiet and spacious when you're coming from other parts of New York, and many of the apartment complexes are attractive and inviting-looking. Only about three miles long, and with a chequered past that encompasses smallpox hospitals and debtors' prisons, it makes an intriguing stroll for anyone interested in architecture or history. (And bonus points to those who find three amusing sculptures by Tom Otterness, collectively 'The Marriage of Real Estate and Money,' in the water on the island's west side.)

Finally, acting on a tip I'd got from a friend, we set off for Fort Tryon Park, home of The Cloisters -- a branch of the NY Metropolitan Museum of Art, housed in a late '30s piece of architecture modeled on actual cloisters of medieval Europe. We took the A train all the way to 190th Street, up where Manhattan narrows into a finger resting on the Bronx. There, an elevator delivers you to street level and the Fort Tryon Park entrance -- gateway to a beautiful, sun-filled oasis.

The park slopes down along a promontory, and amid the blossoms, new grass and overspilling flowers of May, we probably saw its vistas at their best. The Hudson River glowed in the evening light, spanned by the George Washington Bridge to the south. The New Leaf Cafe, an old stone house with a sun-dappled patio, looked irresistible. Truth be told, I was glad we arrived too late to see the collection at The Cloisters. So may the next odyssey begin.