Its famous points are fishes, flowers and ponds.
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Xihu
Hangzhou's most famous scenic sight. It is traditional to see the 10 Scenes of the West Lake and 10 New Scenes, and thousands of the visitors dutifully do so every year. However, these particular sites are overrated, and often seasonal (Snowfall Over Broken Bridge, etc.). Rather than make a checklist and walking back and forth looking for them, simply spend a clear day wandering the circumference of the lake and the causeways, take a ferry to the islands, and you will probably cover most of the sites anyway. The lake is quite large: the walk around it is about 12 km long.
南屏晚钟, Nanpingwanzhong
A powerful bell in a temple on a mountain, rung at dusk. One does not need to visit the bell, it can be heard across the lake.
雷峰夕照 Léifēngxīzhào
The pagoda (see below for full description) is lit up at night. It is best viewed from across the lake, for example from the spot indicated here.
Lesser Yingzhou Isle, 三潭映月 Sāntányìngyuè
Built in the early 1600s, this is the largest island on the lake. When there is a full moon, candles inside the pagodas are lit, and in the candle light it appears as though you see the moonlight (if you are romantic enough to see it), hence the name.
Lin Biao Hangzhou Palace (林彪杭州行宮)
A secret military command center built by Lin Biao in April 1970, hence the name "704" project. The underground tunnels cover more than with many heavy doors that could withstand nuclear and gas attack, and an elevator that directly reaches Lin Biao's bedroom.
皇山公园 Yuhuang Shan Gong Yuan
One of the least-visited sites in Hangzhou despite its somewhat central location. The main temple on top of the hill offers a wonderful view of the city and lake below, and has a restaurant next door. There is another temple partway up the hill. The area can provide a quiet escape and a nice hike, as well as the chance to visit one of the few Daoist sites in the area (most other local temples are Buddhist). It is located directly south of Leifeng Pagoda. The main entrance isn't far from the Silk Museum. If you are playing along with the "10 Scenes of the West Lake" scavenger hunt still, the one that applies to the top of this hill is "clouds flying over Jade Emperor Hill".