It's cheaper to book air tickets in advance. You can look at hotels in Xiamen to save some money. It's recommended to live in Zeng Cuo An Village, a very literary place, which is not expensive and has a feeling, but it may take more time to go to some places.
As for your plan, it's ok to visit around Xiamen on the first day, but if you want to go to Zhongshan Road at night, it's better for you to choose to live near there. There are many snacks in Zhongshan Road, and now the famous Taiwan Province Food Festival is opening. There are too many snacks on Zhongshan Road, so you can slowly find your own food.
The next day, Xiamen University and Nanputuo will take about one morning. Snacks are vegetarian cakes in Nanputuo, but it seems that Xiamen University doesn't allow tourists to enter now. In the afternoon, you can take a ride in Baicheng, Xiamen University, just a few stops. There is a beautiful beach, and the Hulishan Fort is not far away. The ticket inside is quite worth seeing. Then there may be no snacks on this day.
On the third day, I went to Kinmen and Gulangyu Island. Kinmen is Taiwan Province, but it's just a walk. There's nothing special. Please recommend a sign-in book after entering Gulangyu Island. There are many interesting small shops on Gulangyu Island. You can buy a sign-in book and stamp it one by one, which is more memorable. As for snacks, Mazi on Gulangyu Island, Zhang Sanfeng milk tea and a yogurt shop have forgotten their names. . Fried milk, hairy crabs covered with gold and silver can be eaten, as well as local bamboo shoots frozen in Xiamen, fried oysters and the like. If you buy special products, you can go to Huang Shengji. There are many people, but it is worthwhile to queue up.
Actually, Xiamen tourism means watching the sea and Gulangyu Island. The sea in Xiamen is really beautiful. You'd better get up early on the fourth day to watch the sunrise on Gulangyu Island. The sunrise by the sea is very delicious. Gulangyu is a more romantic place in literature and art, so it takes some time to feel it. For example, walk around the streets and lanes, and remember never to leave when you get to the business district. There are many beautiful places, and there will be fewer people who can stroll around the alleys slowly. The apartments in the world can be seen, and the buildings are beautiful. There are many cafes converted from villas, which are also a major feature. People in literature and art generally like it here. As for living in Gulangyu, Gulangyu's, There is a small building called Listening to the Sea, which is near the sea. I recommend it a little.
If you have time when you return on the fourth day, you can go to Jimei School Village. The buildings there are very beautiful.