Hey, I just did a trip to those very places earlier this year.
Shanghai: We flew into Shanghai and stayed in the city for 3 days. I honestly couldn't tell you what I liked about Shanghai and I'm not sure if it's because I was trying to catch up from the jet lag or if the city itself didn't wow me because of the smog. Its worth seeing, for sure, and some areas are pretty neat so I need to go back, without the jet lag to truly give my impression. The city is huge, we stayed a few blocks off the bund near a metro stop. Do use public transportation there. It is cheap and it's very very good. We then stayed one night at each hotel at Shanghai Disneyland. The park is huge, but there doesn't seem to be that much to do so 2 days should be more than enough. I actually preferred the toy story hotel to the Disneyland hotel and we had a castle park view but unfortuently the smog made the view less than spectacular. Now here is where I wish I had done something differently. We flew from Shanghai to Beijing on the earliest flight. I think it was like 7am..
Beijing: We got into Beijing around 9am or so and were to our hotel downtown Beijing by 10am. We stayed at the beautiful Hotel Jen by Shangra la. It's brand new and in a high rise across from the famous CCTV building "the pants" . We spent our first day doing the must sees: Tianamen Squae, The Forbidden City and the surrounding area.. We didn't do too much this night as I was sick and tired trying to fight off a slight cold I had picked up my last day at Shanghai Disney. The next day was up and early at 5am.. this is the reason we came to Beijing. The Great Wall. It had rained all night so we woke up to the most beautiful sunny sky. We hired a highly recommended private driver to take us to the wall. He suggested we leave at 6 or 7 to get to the wall before the buses of people show up so we left at 6! Our driver spoke great english and was a pleasure to be around. We got to the wall with maybe 3 or 4 other people there. It was our private time on the wall we joked. It lives up to the hype. In fact of all the major things I've seen in the world, which is a decent amount, its my favorite. It's truly incredible experience but its a lot of climbing steep steps up and down. Buyer beware. After the wall we headed back to beginning to see the Temple of Heaven before heading to the airport that night for a flight to Hong Kong.
Hong Kong: We stayed at the lovely Cordis Hotel in Mong Kok. It's right on the MTR Mong Kok stop that can literally take you everywhere and anywhere. Hong Kong MTR is the best subway in the world. It's super clean, fast, cheap and organized! Hong Kong is an incredible city. It blows Shanghai and Beijing away, imo. We were here for 3 nights before heading over to one night at Hong Kong Disneyland Explorer Lodge. This hotel is awesome and the views out the back are stunning. Hong Kong Park itself is a little underwhelming with not a lot to do but it is the most beautiful castle park you will ever see from a natural settings perspective. To be surrounded by the mountains in that tropical climate is truly amazing. One day is more than enough here.
From there we fly to Tokyo for 12 days of fun.... We did all the asian parks.. love them all in different ways... Shanghai is my least favorite though... Let me know if there is anything specific I can help you with!