Last time i think 2 yrs back. But hv stayed in taiwan for a period of time, during which taipei became my weekend hunt whenever am too tired for longer trips
Xi Men Ting is a young people's place, visit during daylight hours, esp. weekends. U might run into new celebrities performing there. remember look for a "ah zhong mian xien". u'll notice lots of pple staying around & eating mee sua in xi men ting. try it...yummie ;p
if u're the shopping type, u can vist xi meng ting during the day and take MRT to Shilin night market at about 5pm. There are lots of nice food in shilin, but hv to had early dinner to avoid the big dinner crush.
yang ming shan can be reached by a bus (specially travel to yang ming shan) from taipei train station, u can either walk to the train station from ximenting (15 min - 30 min) or take a MRT (1-stop i think) depending on where u stay in ximenting. the journey is about 1 hr. expect a jam on the way up & down. Hv to try your v. best to go as early as possible for the yang ming shan trip to avoid morning jam (up) and evening jam (down). u'll need at least 1 day in yang ming shan. There is a loop bus service on yang ming shan or u can hike. if u go during dec, choose warm clothings. coz if happen to hv a cold front, temp can be in single digits.
danshui is mainly eating lor... spend 1/2 a day there. its kinda tough to mix with ye liu. one way i can think of is take MRT to danshui v. early & catch bus to ye liu. then go back to danshui in late afternoon. coz nothin' much in yeliu except rock formations. then u just hv to skip "jilong", famous for eatery (again ;p)
around taipei, my fav is jiu fen. very nostalgic little town. can be reached by bus from... erm.. . a train station, (forgot the name liao, need me to check out?). it take train to that station & transfer to bus or cab. u route will take u up a mountain & then down the mountain. i've some postcard pics of jiu feng, u wanna me email to u?
in taipei, i like shilin night market (the old one, hvn't been to new one yet). lots of nice food. & i also love danshui, though didn't go so often as 1hr + MRT ride (like pasir ris to boon lay).
ximenting is boring to me as i'm a guy..haha. only go there to see mei mei
and go "muchuan" ming ge chang ting. other interesting place to visit:- "WuLai", drink tea & see water fall. think there's hotspring there too, couples-friendly as well..heh heh. (prefer hotspring here to yang ming shan).
and another "mt. Kong", also famous for tea i think.