I don't know when you arrived on the first day. If you arrive during the day, you can stroll around Zhongshan Road in Xiamen, go to Lujiang Hotel at the ferry terminal for tea at night, sit in the open air and enjoy the beautiful scenery on the lower shore, and then take a boat to Gulangyu. However, you have to book a hotel in Gulangyu. Some private coffee houses are very comfortable and clean.
You can get up the next day and eat fish ball soup, a famous snack in Gulangyu, and then go back to Xiamen by boat. You can play all the way to Nanputuo, Xiamen University and Huandao Road. You can eat seafood at the seaside of Huandao Road in the evening. Then you can sit in a bar or cafe. Go back to the hotel.
On the third day, you can choose to go shopping or go to the hot springs. Shopping suggestions are to go to the train station, the city trade or SM shopping plaza. The hot springs can go to Sun Moon Valley. If you can't go to Zhongshan Road on the first day, you can go to the pedestrian street of Zhongshan Road for a walk and eat some snacks. Ding 'an Square can also go shopping. Now there is a 616 food street where you can taste many special snacks. Satay Noodles at Ding 'an intersection suggested trying it, which is a feature of Xiamen. There are also five-spice rolls.