Sounds like a plan, but the earlier you can procure the train ticket the better.

If you have a free evening, especially early in the week in Shanghai, try to walk along the Bund in the early evening. There are also cruise boats (I haven't done this, but a local came close to leading a group of us there during a recent visit) and a selection of rather expensive restaurants and bars in beautiful historic buildings on the Puxi side. Try to also go to one of the view places to enjoy the lights on a clear evening, ideally late day to sunset to night, so time your drink at the Park Hyatt of whatever carefully or plan to use your hotel's top-floor concierge lounge at a good time.

The "history museum" and elevators in the distinctive tall toy building on the Pudong side are open into the evening. You can also walk along the river on that side around the aquarium and Shangra-La (?) hotel, near Fashion Mall.

Some of the art galleries are open late-ish and I think the same is true for the little city museum in the basement on the corner of People's Park. The main Shanghai museum might have extended hours some nights. Your visit in April is before the annual free period when lines are impossibly long.

You can also see a lot of the French Concession and Xiandu (spelling???) at night. These are also good areas to find somewhat upscale restaurants.