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Photo: David290, CC BY-SA 4.0 via Wikimedia Commons
On the shores of the southeast side of the lake and built in the year 977, all that remains of the original pagoda is the crumbling foundation, viewable from outside the glass case that it is housed in (Pagoda Remains Memorial Museum at the bottom floor of the pagoda). With escalators, elevators, and a totally new pagoda places on top of the foundation, there is not much to see within the pagoda, which was rebuilt in 2000. However, the view of the city skyline is one of the best from here, and some of the smaller seating areas around the perimeter of the pagoda have a nice breeze and view of the structure. One of the 10 Scenes of the West Lake is "Leifeng Pagoda in Evening Glow", but this is best viewed from a distance (across the lake) just after sunset. The entry fee for the Leifeng Pagoda ¥40/person (Mar 2018) and it's not original, just rebuilt. If you don't pay to go in, you can still take pictures in front of it.
The Leifeng Pagoda is a five-story, eight-sided tower located on Sunset Hill south of West Lake in Hangzhou, Zhejiang, China. Originally constructed in the year AD 975, it collapsed in 1924 but was rebuilt in 2002. Since then, it has become a popular tourist attraction. A view of the original pagoda at dusk was one of the famous Ten Scenes of West Lake and it was notable for featuring as a location in the Legend of the White Snake.
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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.
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.
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.
花港观鱼, Huagangguanyu
Its famous points are fishes, flowers and ponds.
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.
柳浪闻莺 Liǔlàngwényīng
A large park at Qingbomen (清波门), when orioles can be heard singing.