Xiaoliuqiu sounded like a good idea to escape from the city one more time though, situated in front of Kaohsiung, it’s a long trip from Taipei. The ferries departures from Donggan and seems to be several ones in a day, you can get more info here.
As in the other Taiwanese islands, the best option is to rent a scooter and explore by your own. Xiaoliuqie offers ships, temples, good food (I specially loved some kind of meat balls there!), a eccentric church and in general, a peaceful atmosphere:
A couple of must do to take in account. See the sunset from Geban bay
And join to some tour to do some snorkelling as you might be lucky and see some big turtles!