Try Diane, she has many satisifed customers, both Taiwanese and westerners. We lived in the US for a while so she speaks good English, and she also worked as hair dresser full time for over 4 years in Sweden (speaks good Swedish, too), so she knows western hair and hair styles. She also worked in Hong Kong for a short time.
She's conveniently located in the middle of Taipei, just 3 minutes walk behind SOGO towards Civic Blvd. By MRT, get off at the Zhongxiao / Fuxing station on the blue line, taking the SOGO exit (4). There's a (bad, I drew it) map on her web-site (see below), but basically you walk in the direction of Dunhua for about a hundred meters until you hit Da'an Rd. Turn left on Da'an towards Civic Blvd. Pass a 7-11 on your right hand side. The last lane on the same side as the 7-11 before you get to the Family Mart convenience store (which is on the opposite side of Da'an) is lane 31. Turn right into that lane and you'll find Diane about a hundred meters down, on your right hand side just before the intersection.
Phone: 2778 4733
Address: Da'an Rd., Sec. 1, Ln. 31, No. 31, 2Fl.
She prefers time appointments to just dropping by, so give her a call. She's open till 8 pm Wednesday through Sunday (Mondays and Tuesdays off).