I'm not going to "scold" you for visiting China on a tour, since you have already committed to going this way. I would, however, like to offer you some suggestions for Shanghai.

If you just have one afternoon, I would spend the first two hours hours at the Shanghai Museum. I would focus on the marvelous jade collection, and whatever else catches my fancy. My sons and I spent four hours in the museum, but you can cut it down if you have limited time.

Then I would head outside, and walk along the Bund. There are some amazing building there that were built about a hundred years ago, and yes, you can generally go inside.

If you can, I would see the circus, which, thank goodness, does not include animals. And we had fun having massages. We ran into some other Americans who had amazing foot massages, complete with "foot-slapping"--I regret that we didn't have time for that.

Shanghai's Bund at night is a fantasy of lights until 10pm. The river cruises leave frequently and are not expensive.In the Shanghai Art Museum take a look at the Chinese paintings and the stamps or chops which I found so interesting. The gift shop there sells high quality items.
Hangzhou is a lovely city and you'll enjoy your time on West Lake.
Friends who flew Hainan from US east coast gave them good reviews.
As mentioned above, get a hotel business card in Chinese and English with their address when you check in and keep it with you.

Also in Shanghai, go for a walk in the tree lined historical French Concession.