I will arrive at Shanghai Pudong Airport around 12:20am.

Yes, beside the cab, you can also take the airport shuttle bus Night Line to get to East Yan'an Road Middle Zhejiang Road (nearby People's Square). The operating hours of this bus line will until 45 mins after the last flight. So you can catch it. The ticket fare is about CNY 30 per person. After arriving, you can take a cab to the destination. :)