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Lishui is surrounded by mountains. Most of them could be climbed, despite not being official hiking trails. Easiest access to the mountains is behind the railway station (200 m west from the Station, there is a tunnel). Local villagers grow fruit (tangerines, peaches, mulberries, bayberries) in those mountains, so there are plenty of trails used by farmers. You'll also pass through many old villages with absolutely stunning views and virtually no tourists (since the only 'official' hiking spots are Baiyun Shan, Nanming Shan, Dongxiyen and Kuocang Ancient Rd.) Take with you water, snacks and a hiking stick to scare off the snakes (there are cobras in those mountains, so be careful between May and October).
应星楼
Beautiful building with a focus on astronomy. There is a small rotating exhibition on the ground floor and the 2nd and 3rd stories contain an exhibition about Chinese astrology. Climb up further and there's some kind of star show that doesn't run very often and on the very top floor you'll find a small temple with fantastic views of the city and waterfront.
丽水市博物馆
Large museum with lots of different exhibitions, including history, animal life, the 3 treasures of Lishui (pottery, sword-making and stone-carving). Plan to spend a couple hours here. Small gift shop.
中国丽水摄影博物馆
Two-story museum with rotating exhibitions with photographers from around the globe. There is also a permanent exhibitions about cameras.
庆元县香菇博物馆
处州公园
The Old Pagoda 厦河塔
A Ming Dynasty pagoda in pretty good condition. The best time to visit is sunset, when one can take full advantage of the western-facing view of the city and its mountains. Make sure to wander around a little, and check out the connected temple, which can be accessed through a small shrine half built into a rock, off the right of the path up to the temple.