(In taipei, just take train can reached lo)
Danshui also a nice place too.. can take a stroll at the shop located at the side of the river, take boat to Fisher's Dwarf featuring the bridge and eat seafood.. lolx
(In taipei too, just take train can le.)
If got time in the afternoon can go Jiufen too.. Nice place for photography too. Teahouse, old street, eating and shopping...
(From Taipei take train to Ruifang station i think.. Took around 1++ hour trip)
Not sure your packaged tour include these location or not ..
As for night activities, look for night market in Taipei such as Shilin night market or Huaxi night market.. I just went last year, feel like going again..