Hi Mark, I spent 2.5 weeks alone in Taiwan last year, and I met people in the youth hostels, a lot of whom spoke both Chinese and English, and were travelling alone too. Everyone is super friendly out there too :-) Just stay at backpackers hostels etc, and some of the staff will speak English and help you out where they can.
I can recommend:
Sleeping boot backpacker Hostel (NO.73., Jinfeng St., Hualien, City, 970, Taiwan., Hualien, Taiwan 970)
Go to Hualien, and visit Toroko Gorge from there. The guy who runs this hostel speaks very very good English, and he loves to make sure his guests know what they are doing and where to go :-)
In Taipei, I can recommend
Taipei Backpackers Hostel
2F., No.14, Lane 11, Taiyuan Rd., Taipei
Again the member of staff who helped me spoke really good English and helped me a lot with where to go and what to do!
These are just the two I remember that I stayed at...but in each hostel I met travellers from South Korea, Japan, etc...who knew English and for some, their English was better than their Manderin!
Hope this helps. Enjoy your trip. It's one of my favourite places :-)