Cosi o Cosi is a decent little Italian restaurant on Dunhua south road, section 1 and the food is generally quite good there. Some stuff is slightly over priced, but most of it is quite tasty. They also have a large selection of imported beer for those interested in that. Their phone number is (02) 2771-5883 and they’re open seven days a week from 12.00 to 14.30 for lunch and 18.30 until 23.00 for dinner.
If you’re not familiar with Taipei, then take the blue line MRT to the Zhongxioa Dunhua MRT station and then exit via exit number eight. Walk straight up the road you get out on (Dunhua south road) and keep walking for about 3-4 minutes. You should walk past a a Häagen-Dazs before you get there.
You can find more details on their Facebook page.
Update: I would say that Cosi o Cosi has gone downhill over the years and we don’t tend to go there any more. At one point they had a Gelato place a few doors down, but that didn’t last too long, most likely due to the high rents. However, it’s one of the older Italian restaurants in town.