On top of Xisheshan Hill, inside Sheshan National Forest Park, there's a small astronomical museum set in what used to be the historic Sheshan Observatory—one of China's earliest modern astronomical research sites.
The building is the main draw. French-style, with a dome in the center that still houses a restored 40cm double refracting telescope, once among the largest in Asia. Inside, things are pretty simple. A few exhibition rooms, old instruments, and a lot of archival material.
What makes it worth the trip is everything around it. Right next door is Sheshan Marian Basilica, a hilltop Catholic church mixing Romanesque and Gothic styles (no photos or videos inside). Between the church, the observatory, and the surrounding forest, it's easy to spend a slow half-day just walking around. The museum is open daily from 8:30am to 4:30pm. Tickets are only 12rmb. The basilica is free to enter, just don't disturb if there's an event.
Getting there takes a bit of effort. The nearest metro is Dongjing Station on Line 9, but you'll still need a didi for about 6 km into the hills, followed by a roughly 20-minute uphill walk. It's easier to take a didi all the way there.
It's not a big, modern science museum, and it's not trying to be. On a quiet day, it works more like a small escape from the city, with a bit of early Shanghai science history along the way.