what the interesting place to visit at xiamen? Ideal month?

You can go to Gulangyu Island, South Putuo Temple, Zhongshan Rd Pedestrian Street, The Road around d the Island, Zeng Cui An, and Jimeixue Village.

Well, besides the city, you are suggested to pay a visit other attractions nearby, like Tulou in Longyan city, and Mount Wuyi.

As for ideal month, Mar. -May & Sep. & Oct. is a good time.