And I hadn’t even gotten to the mountains.

Logistics made far more sense once I gave myself over to the best organized and most helpful tourism department I have encountered in all my many months of travel. The ladies behind the counter steered me to a three-day Tell-Pass, which for 210 Swiss francs (about $216), gave me unlimited transportation on boats, trains, buses and cable cars in Central Switzerland — and helped with my general sense of sticker shock. Considering that most mountains cost $100 to get to, and get up and down — and even beer in Switzerland can set you back $10 — it was an unequivocal steal, even for someone moving at the quite reasonable pace of one mountain a day. I made it up four, for a saving of some $200.

The friends you meet on mountaintops

All I’d heard coming to Lucerne was that I needed to go to the top of Mount Pilatus, the area’s signature peak, that, according to legend, was once home to a dragon with healing powers, and may or may not contain the grave of Pontius Pilate. All I’d been hearing from the tourism office during my first few, very rainy days, though, was that the summit would be shrouded in clouds and not worth my money and effort.

Restless to get out of the city, I finally took my chances on the lower-elevation Mount Rigi, which was hardly a downgrade; it promised a glorious morning boat ride to Europe’s oldest mountain railway, and a hiking trail lined with wildflowers. On the way up, I had spotted an intergenerational trio of American women travelers who seemed to be having a ton of fun. I tried out my go-to pickup line for making friends on mountain summits: “Hey, would you like me to take your picture for you?”

Within minutes we were bounding off to a lookout point, making plans to get a beer at a ski lodge cafe and debating whether or not we felt sorry for the cows grazing on the slopes with bells ding-donging on their necks, as if being followed by Will Ferrell in that Blue Öyster Cult “Saturday Night Live” sketch.

One member of the group, Minnie Nguyen, who goes by Nhi, told me she’d gone up to Mount Titlis the day before — another mountain I had wanted to see but had vetoed because of bad weather. She couldn’t see a thing, she said, but how incredibly glorious it was to walk out on a suspension bridge in a canyon in the middle of a cloud: “It was like flying in an airplane without any windows!”

Communing with dragons

It took me another two days to get to Mount Titlis, the area’s only publicly accessible glacier, at an altitude of 9,900 feet. And while the views were as spectacular as promised, the experience felt like going through a tourism obstacle course. You step off a rotating cable car into a blue-lit ice cave, walk across the suspension bridge, go up and down “the Ice Flyer” (a ski lift) and go home — more engineering than nature. As a snowboarder, the winter wonderland of mild sledding slopes didn’t appeal. But for families, it’s perfect. I nearly cried watching two young boys from Goa touch snow for the very first time.

Spurred on by Ms. Nguyen’s “rain or no rain” sunny attitude, I also headed to Mount Pilatus on an iffy weather day, ascending via the world’s steepest cogwheel railway (48 percent gradient). It really did look like the realm of dragons, with views of 73 neighboring peaks from barren cliffs at the top of the world. On a platform, a trio of musicians played wooden alphorn wind instruments, which stretched the length of two people, stacked one on the other, and echoed to the top of every lookout.