If you’re traveling from the United States, your flight into Taipei will likely arrive in the evening. Check into your hotel, either the 303-room Mandarin Oriental, which has a traditionally opulent décor, or the 86-room Capella, which has a chic contemporary style. Both are in the upscale Songshan neighborhood, and both have full-service spas, outdoor pools and excellent Chinese restaurants, among other dining venues. (It could be fun to stay at the Mandarin Oriental first and then finish the trip with the Capella.)

Take two full days in Taipei to explore. First visit major landmarks like the ornate Longshan Temple, the Taipei Botanical Garden and Liberty Square, a vast plaza that culminates in the towering Chiang Kai-shek Memorial Hall. Just across the street is one of our favorite restaurants in town, Lepu Lounge, which serves a gourmet tasting menu in a tiny Japanese-style house. After lunch, return to your hotel for time to relax by the pool or have a spa treatment. The craft cocktails at the M.O. Bar are justly acclaimed.

On your second day, visit the National Palace Museum, home to imperial treasures carried out of Beijing’s Forbidden City during Chiang Kai-shek’s flight from the mainland in 1949. It can be crowded, but it’s highly worthwhile. In the evening, consider doing a guided food tour of one of the city’s famous night markets. The Travel Office can make arrangements. (In fact, advisors can organize an array of customized Taipei tours tailored to a range of interests, including cuisine, history, art and shopping).

Head southwest with a driver, making stops at the fascinating Zhunan Snake Kiln (holder of a Guinness World Record), the unexpectedly fantastic Sanyi Wood Sculpture Museum and the ruins of Longteng Bridge. Turn east into a steep mountain valley and wind your way to the spa town of Guguan.

On a hillside just above the village is Hoshinoya Guguan. Reminiscent of a Japanese onsen (hot spring) resort, it has 49 immense accommodations overlooking forested mountains. Each room has a private onsen bath, and the resort also has extensive gender-separated public baths, with both indoor and outdoor pools.

Take a day and a half to just relax here, enjoying the sublime hot springs, the cabana-lined swimming pool, the creek-laced gardens and the commendable restaurant, which serves a Taiwanese kaiseki dinner (à la carte dinners are also offered, but they’re served only in your room). Active sorts can hike up the mountain trail that’s right outside the hotel’s back door and/or head into town.

Depart Guguan and wind your way through the mountains to Puli, where you can see the huge and futuristic Chung Tai Chan Monastery; the Goang Xing Paper Mill, one of Puli’s last artisan papermakers (hands-on workshops available); and the Paper Dome, a unique chapel designed by Japanese architect Shigeru Ban.

Continue south to one of Taiwan’s great beauty spots, Sun Moon Lake. The best resort on its shore is The Lalu, with 96 midcentury-modern-style accommodations, most of which afford stupendous views — like something out of an old Chinese landscape painting (avoid Courtyard Suites). The hotel’s stunning infinity pool is reportedly the longest in Taiwan, and nearby is a delightful tea house that serves dim sum on a terrace or in indoor-outdoor pavilions. The hotel also has Chinese, Japanese and Western restaurants, plus a spa.

Take two days to enjoy the lake. Be sure to have a driver-guide take you on a tour of its circumference to visit the orange-roofed Wenwu Temple, the Indigenous town of Ita Thao (try some traditional millet wine) and perhaps the Ci’en Pagoda. The panorama from its upper floors is sensational, but the uphill hike to reach the tower can be tiring. Finish at the strikingly modern Xiangshan Visitor Center, a great place to stop for an ice cream before returning to the hotel. The Travel Office can also arrange private lake cruises and day trips to various nearby attractions.

In addition to sightseeing, leave ample time to relax at The Lalu and soak in the view.

After a leisurely breakfast, return to Taipei and check into the Capella. After you settle in, take the hotel’s Songshan Reverie walking tour, designed by the general manager. It shows you an insider’s view of the neighborhood, revealing little treasures like a stationery shop hidden in an apartment building, a crumbling farmhouse and, unlikely as it sounds, a butter-cookie speakeasy. In the evening, take advantage of the three bars at the hotel’s Glasshouse building, a short walk from the main entrance. Playback, in the cellar, often has live music.

On your last full day, explore the historic Ximen neighborhood and stroll up Dihua Street, a charming set of low-rise blocks that house fashion boutiques, craftsmen, antique shops, cafés and cocktail lounges (the atmospheric Spring Breeze at 333 Dihua is a favorite watering hole). Be sure to leave a little time to unwind by the hotel’s pool and guests-only Living Room lounge.

If you have more time, you might take an additional day or two to walk up the steps of Elephant Mountain, which affords panoramic views of the city centered on the iconic Taipei 101 skyscraper. Around the base of Taipei 101 are numerous designer stores. You could also make a short day trip to Yangmingshan National Park, just north of the city, for some hiking, and/or Yehliu Geopark, known for its surreal mushroom-shaped rock formations by the sea.