Taipei is far more than just the home of 2 million people and the city center of Taiwan. It is a city where you can explore great nature just around the corner. The national park of Yangmingshan is a nearby place you cannot afford to miss out.
If you go to Lebanon you really should take the advantage and explore a bit of the country. During my trip to Beirut I also went to the city of Harissa and Byblos and that are two places I strongly recommend to visit.