Some random ideas:

For an expensive drink in an interesting place, there are bars (and restaurants) in some of the renovated historic buildings along the Bund. There's also a very high bar with views in the Park Hyatt on the Pudong side, but be prepared for waits for the elevator and a long taxi line in the evening.

Check out the lobby/public areas of the Peace Hotel (Fairmont now after renovation) and its annex. On the "far" end of the Bund beyond the Peninsula, there are a couple interesting historic hotels; another one is called something like Park Hotel, right across the street (Nanjing Road?) from People's Park (which has a quaint little amusement park). If you walk from there toward the Bund, there's a big old department store on the corner (another interesting historic building, but I was disappointed when they removed the huge fish tank in the window) and then a stretch of street that's closed to traffic in the early morning and filled with people doing group exercises, dancing, etc. You'll also see the group exercise/dance performances (I've been told that you can pay a bit to join) and kite flying along the Bund.

For shopping, explore the antique stores (old books, chess sets, and other small items) along "philosophers' (? or is it poets'?) walk" old pedestrian street near the Bund and the creek. Further back and almost along the creek, there's a big cluster of modern art galleries, mostly in old warehouses. The French Concession is good for boutiques while there are high end stores around Xiantendu (spelling???). There's a well known big modern mall over in Pudong.

I enjoy the art museum and the modern art museum nearby (behind the lily pond in the small park, in a modern round building).

Some of the Shangahi Expo buildings are still standing. Much of the area has been turned into a park, so this would be an interesting place for a long walk. Another interesting place to walk is the campus of Fudan University; it feels far from the tourists, but of course has international students and visiting faculty.