what's the most interesting place of visit and activities to do in Taiwan during July to September.

If you plan to go at that time, Ali Mountain is suggested.
Actually, there are diffferent sceneries in different part of the Island. For example, Maokong and Yangming Mountain in Taipei and Xiziwan near Kaohsiuing. It depends on which place do you perfer.
July to August is the typhoon season in for the island, so it is not suggested to go at that time. October is the best time.