All eyes may be on China, with less than a month to go until the Olympic Games. But dynamic Taiwan – regarded a rebel province by Beijing – is worth a side trip, says Andrew Spooner

There's big and then there's Taipei big. I've just spent the morning at the top of the Taiwanese capital's Taipei 101 which, despite an unfinished tower in Dubai, remains the tallest completed building in the world.

The views are immense; endless runs of streets unfolding like miniature circuitry. But it isn't Taipei 101 that creates an imposing air. For that I need to go to the Chiang Kai-shek memorial and stand at the feet of the Chinese nationalist leader's statue. "He is our national hero," says my guide, Mr Jeng. "This is almost a holy place."

I don't doubt my guide as I gaze up at this huge eulogy to Taiwan's founder. In fact, such was the weight of Chiang Kai-shek's shadow that Taiwan was still considered "China" by the UN as late as 1971.

These days, Taiwan is considered a rebel province by Beijing. Yet, with eyes on China and the Olympic Games, democratic Taiwan is still fiercely independent and dynamic. It is also keeping up with the mainland's furious development – and nothing symbolises this better than its new high-speed bullet train.

"The line links our two main cities, Taipei and Kaohsiung," says Mr Jeng as we climb on board the sleek train in Taipei's main railway station. Modelled on the Japanese bullet train, Taiwan's effort hits the same 200mph-ish speeds, thereby reducing travel along the length of this 245-mile island to a mere blip. "It has been built to open up the country to tourists and businesses," says Mr Jeng.

So what is actually being opened up? The western tranche of Taiwan along which the train travels is a dense, ugly, urban twist of factories, concrete tower blocks and flat plains. This is where Chiang Kai-shek's Chinese nationalists, the Kuomintang, sought refuge from Mao's marauding communists . They came in their millions creating a prosperous community that is distinctively Chinese.

The eastern run of Taiwan, where I am heading, is much more intriguing. In a stretch of mountains that reaches down the length of the island, this slice of Taiwan is filled with forests, beasties and indigenous peoples who have more in common with South Pacific islanders than the dominant Chinese.

"We'll take the train to Chiayi," says Mr Jeng. "It's about halfway between Taipei and Kaohsiung in the south. From there it's only a short drive into the mountains." As we head into the distant peaks, switchbacks and deep thick woodlands become the defining views. The contrast with the industrialised western Taiwan couldn't be greater.

Our first mountain destination is the resort town of Alishan. "This place is very popular with local people," says Mr Jeng as we arrive in the middle of a thick pea-souper. Alishan has a mystique all of its own. Tiled, sloping roofs, teahouses and dense forests mingle with hordes of Taiwanese visitors. We stop for a plate of noodles and swift pot of tea but are soon on our way.

The narrow road takes us deeper into the mountains, the views of gorges and craggy peaks getting more dramatic. Our lunch involves earthy tastes – omelettes with rosemary, dense pork stews, mounds of brown rice – far from the dim sum and noodles on the west of the island.

"This village, Wutai, is home to the Rukai people," says Mr Jeng, as we arrive in a cluster of buildings strung along a high mountainous ridge. The usual sweeping roofs of Chinese architecture has been replaced by slated buildings and statues of hunters.

Accommodation is in guesthouses and homestays. "You'll be staying with the village chief, Ragaro," says Mr Jeng. The friendly chief and his wife don't speak English but they welcome me in with smiles. "This is his skull collection," says Mr Jeng as Chief Ragaro proudly shows me hundreds of boar skulls. "A Rukai warrior's status is measured by the number of skulls he has."

As I wake up the next morning, the view from my window across the mountains is bewitching. I sit and gawp for a while, absorbed and becalmed. Chief Ragaro's wife brings me bowls of pork meat and rice and soupy green tea.

Taiwan for most people is a place of grand buildings and hi-tech projects. For me the most memorable things are the diversity of its people, the beauty of the mountains and the humbling hospitality. Who needs big when you've got all that?