I have never gone to Shanghai to be a tourist. It has always been a transitioning point in my travels. But, I have been to Beijing a few times for work. And, I have done many of the tourist things there. I really do not like the big city life here in China. But, there are many things that are interesting in Bejing to see. The problem with giving tourist advice of things to see is that your interests and someone else's interests could be very different.

For me, I hated the Forbidden City. It was far too commercialized and never really gave me that "stepping back in time" feeling I like to get. You basically get to see some old buildings without much of the history. The Great Wall was fun for me to visit. But, others will say, "Yep. It is a big wall" and move on. The National Museum was not as good as I thought it would be. For one thing, you never know if you are looking at replicas or actual artifacts. And, it reall does a poor job in articulating China's 5000 year history. For a National Museum, I think it could have done a much better job.

Some of the lesser known spots to see in Beijing that were interesting to me were:
The Military Museum: I am not sure it is open yet from it's renovations. I only got to see the outside exhibits.
The Ethnic Cultural Park neak Olympic Park: Designed for the Olympic crowds, it is falling into some disrepair. But, it is still quite interesting to visit
The Houtong Museum: This is a very small museum showing life in the old communities of Beijing that are rapidly disappearing due to modernization. And, it is a bit hard to find.
The Summer Palace was nice to wander through on a warm day.
Sun Park was good to see how Beijing redeveloped an Olympic site and transformed it to be used long after the Olympics disappeared.

I recommend that you look at the website TripAdvisor for travel sites in China. It is a good jumping off point in planning travel in China for things that might be interesting to see and things to do.

Best of luck to you.

my town is the best place in all of China...  Zhanjiang, Guangdong. From here you can do anything you need to do throughout China, while enjoying a little more peaceful quiet lifetime at home......airport to go to Beijing if need be.... train or bus to Guangzhou, Shanghai the same...  good transport if needed. best to just stay home and deal with it from here. emergency, can get there.

best weather, near cleanest air, reasonable rent, and great food .....  what more could you ask for?

If you haven't been to the bigger places in Beijing (National Museum, Great Wall) then do it. Try your best to go to a section of the Wall other than Ba Da Ling. It'll cost more cause you gotta get a taxi to the next closest section, but oh is it worth it.

The National museum is something you need to prepare to do for 4-5 hours, and you won't finish everything even then. It's way better than any museum you can find in any other city in China.

Yuan Ming Yuan and Yi He Yuan are super awesome. Just go there and take in all of the water, trees, flowers, and space. Try to imagine what it was like long ago.

My biggest mistake was not doing either of those early enough. I think if you stay in China for at least a year you should at least go to one of those.

You bringing the family ? Then make sure they are all does up on needed vaccinations (wife cluded in) 

Rather than Shanghai, aim for Suzhou. Same advantages, less disadvantages, business friendly environment, a bit cheaper, and the kids will have some nice spaces to roam around. It's merely 20 minutes away from Shanghai. Suzhou is China,  it's not HK, but the lite version. Zhuhai, Xiamen are great too, for the same reasons. Beijing/Shanghai are crowded beyond reason, no need to pile-up there.

If i were you i would watch out for the autistic kids you diagnosed after 10 minutes,or maybe the stalker ex,don't forget the gangsters either,and the brother in law and what ever else you dreamed up