Places to visit in Xiamen

The "standard" must do sights on Xiamen Island are:

Gulang Yu  - needs a day to get around Gulang Yu Island, as there are many sites on the island.  10 minutes by ferry from Xiamen, cost RMB 8 return.

Nanputao Temple - another major sight in Xiamen, going up the side of a hill, and next to  Xiamen University (Xiada).    Also close to the beaches, which are not bad by Chinese standards - but China will never make it as one of the beach destinations of the world - free, or donation.

Hulishan Fort - also close to the beaches and Xiamen University  - RMB 20.  Built in 1892 to fend off "foreign imperialists", and houses one of the world's largest cannons, built in Germany by Krupp.

Wanshi Botanical Gardens - quite impressive botanical gardens covering a large hilly area - RMB 40.

Zhongshan Lu - street with traditional architecture, with a lot of traditional food available.

Apart from the above, Xiamen is mountainous (well, they are called mountains, but hills really), lareg number of temples, and as mentioned, numerous beaches.  There are also scenic areas around Yudang Lake, and Xiandong / Xianyue Mountains.   

There is more than enough to fill a 2 day visit, but a week would be long enough o see everything.

Personally, I find walking along the paths in the mountains a good way to spend down time in Xiamen.