I have stayed, and had a few friends stay long-term at the Ladoll Serviced Apartments in Jing'An.

They have studios and one bedroom suites. They are fairly compact, but clean, staff generally friendly and helpful, and the location is pretty good (but you will need to bear in mind traffic getting to and from work).

You can get deals (USD100 a night for a one bedroom) through OTAs such as booking.com

A couple of recent reviews on tripadvisor have complained about poor wi-fi, and there seems to have been some problem with water (lack of), but I haven't experienced those problems.

It might be a good place to start out for a week or two while you look around for something once you get there.

Website and trip advisor:

http://ladoll-service-apartment.sunr....net/rooms/#hn
https://www.tripadvisor.com.au/Hotel...-Shanghai.html