Shenzhen is not that bad, actually. it is not a tourist city and it is just a very new city, but you can find something to do. and in december the weather will be not too hot, like spring. I raccomand you to take a walk at Shenzhen bay park, it is near the sea, starting from the Mangrove seashore ecology park, the park is very nice and not too crowded during the week...you have a little daughter, so take a sun umbrella with you if you go there.
There are some very tuorist places, like Window of the world and very close to it there is Splendid China folk village, and then Sea world and Oct harbour...the last tow have many westrn restaurant and there are just turist..but at night they are nice because of the lights and there are some fountain and light shows.
Very famous is also the painting village of Dafen, and if you like modern art you can take a look at the OCT-Loft.
Actually Shenzhen is a very green city, there are many parks, and many mountains..but I didn't visit them yet. The Zhongshan park is very nice and in front of it you can find the Dutch flower market, anice flower market but kind of funny coz it is in european style.
Not so far from Shenzhen there is the Dapeng fortress, I haven't been there yet, but it is in my plan. It is an old village that must be interesting to visit.
There are also some Hakka village, like in the Pingshan district.
I hope this can be useful for you, remember that Shenzhen is a typical very big city, so it takes time to go around, so 5 days can be not that long time for visit it ^^
have a good day and good trip
Monica
Just so other are clear-
You can book accommodations/reservations for the purpose of the Visa Application, then once you get your Passport Back, cancel them do what ever you want. If you stay in a AirBnB, you will need to register as a foreigner at a local police station. But if you stay at any hotel, they take your info and pass it on the authorities and and you don't have to do anything.
I don't see any need to stay in that city longer than needed. Maybe get a flight to Shanghai or Beijing, check C-Trip.
US Citizens can now got a 10 year Visa, 60 days per stay, for almost the same cost as a single visit Visa. Same for Chinese citizens visiting the USA. My father in Law just got his USA 10 year Visa, to visit us in Chicago and also tour the country at his whim. The difference for Chinese is they have to update their info for Chinese authorities every 2 years.
Also, if you are just passing thru China, you get a 72 Hour Visa on Arrival at some of the major cities, Beijing, Shanghai, but Goungzhou not sure...

The visa, once you get it, allows you to go just about anywhere in China (except Tibet among others). Shenzhen does not compare at all with a place like Beijing.
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