What to do with two transit days in Xiamen?

Hi, Carlos. According to my experience, I don’t think you need to hire a tour guide for the whole trip. You can hire one when you need at the particular attractions, like museum, memorial hall and some historic sites. I will recommend you two classical routes.
It is suggested you visit the Gulangyu Island during your first transfer.
You may follow this route on 4 May: South Putuo Temple – XM University – Zengcuo’an Food Court – Zhongshan Rd Walking Street. It is advised you take a taxi to reach each attraction to save your time.
Notably, you need to arrive at the airport at least 2 hours before the plane departs. If the schedule is two tight, then you may ignore the attractions you are not interested in. You may also prepared your trip in advance by collecting information of these attractions on line or asking help for a Chinese friend.