The Lantern Festival in Taipei will being on February 27 and continue until March 8 at Taipei Flora Expo Park (map).
You can take the Line 2 (red line) on the MRT to Yuanshan Station. However, some trains will bypass the station to avoid overcrowding, in which case you should get off at Minquan West Rd. Station and walk to the Expo Park. Buses to Yuanshan and the Expo Park include No. 32, 34, 50, 72, 109, 222, 285, 527, 542, 606, 665, and 685.
Passengers with bikes will not be allowed to enter or exit Yuanshan Station after 3 PM on February 27 and 28 and March 1, 7, and 8. YouBike rental services at Exit 2 at Yuanshan Station will also be suspended.