Is Taiwan (more specifically Taipei) worth visiting?

I'm going to be travelling around China with my friend from June-July and I'm trying to come up with a list of places to visit. I have a Taiwanese friend and the country has intrigued me since I met her. Is Taiwan vastly different to mainland China, as in different enough to warrant a trip there, and how is Taipei for nightlife, cheap accommodation and just general fun for a couple of 20-22 year olds?