Is May a good time to visit Xi'an? Any neighbouring province / sites a must see?

Yes, May is a good time for travelling. In May, the temperature rises quickly. Bright and sunny days are most common. It is generally warm and pleasant. As for nearby cities to visit you may think about Ankang, Hanzhong and Baoji. If you want to go to other provinces, you may think about Sichuan, Henan or Shanxi. Of them, Sichuan is highly recommended.