Taipei is easy-peasy for the solo female traveller
I think Taipei is one of the easier places to travel to as solo female traveller. It's safe, convenient and friendly! Many of the young people speak English so it's not difficult to get help if you need it, and the Taiwanese are always happy to help. Its public transport is easy to understand and use. If you love selfies, nobody will judge you for taking tonnes of selfies in Taipei. I never encountered any issues with safety in Taipei even if it's late at night.
Insider Tip:Definitely get the EasyCard for MRT and bus rides because it's cheaper and more convenient. Taipei's one place you can afford to let your guard down a little and enjoy. Could even see it as a "break" from your traveling.