Is Shanghai Red Mansion a good place/location to stay? Can I get public transit to Disneyland?

Yes! It is adjacent to Huangpu River, Xintiandi, Yuyuan Garden and City God Temple.

To Disneyland, walk northeast for 0.6 mile to South Xizang Road Metro Station. Take metro line 8 to Oriental Sports Center, and switch to metro line 11 to Disneyland. The metro ride takes about 45 minutes, and the fare totals CNY 6. :)