I've been backpack to Taiwan during Nov 2005 with my friends. We've visited to Taipei & HuaLien districts for the 6D5N trip. In Taipei, we've went to places like XiMenDing (we also stayed there), LongShan temple, Ye Liu, Jiu Fen, Taipei 101, CKS memorial, National Museum, ShiLin, TanShui, Wu Fen Pu night market ect. In Hualien, we just managed to visit Toroko National park. The weather was nice (around <=24C) during Nov. It's quite easy and convenient to explore the Taipei city via their MRT.

We stayed at wonstar hotel (but i won't recommend it, instead, i'll recommend 'Rainbow hotel' there) for 1st nite we arrived. we booked this hotel thru local travel agent. We stayed at the other low cost hotel in ximending for the subsequent days we in Taipei.
Taipei is easy to explore via their public transportation (mrt, bus). most of the interesting places like Ximending, LongShan temple, Taipei 101, CKS memorial, National Museum, ShiLin & TanShui nite market can be reached by mrt (its save $ if you buy 1day unlimited ride pass). Ye Liu & Jiu Fen can be reached by bus. Other districts, for example HuaLien can be reach via train (around 4hr++ journey). It's quite important to do your own homework before going backpack there.

This post has been edited by joeyg07: Mar 19 2007, 04:33 PM

should be enough (if you give up staying in 4-5 star hotel)