I’ve only been to Wuhan once, having arrived on a train and then shuttled around by my supplier the entire time (WISCO; the W is from Wuhan, anyone that cares can look up the rest). However, I lived in China for five years and transited through Shanghai very often.
First off: ease your mind. When I first went to China on my “pre assignment trip” I was petrified. It was communist and there’s no alphabet and no one speaks English. Keep in mind that I’d lived in Canada and Europe and Mexico at the point, and was’t a neophyte; China is different. But all of those fears evaporated within the first few hours of being on the ground. You will be okay. Anything that deviates from your plan is just part of the adventure, right?
So arrival at Shanghai, you will clear customs and immigration. There won’t be much conversation with the immigration guy, and customs is about following the green arrows. At worst they’ll X-ray your stuff while ignoring the monitors.
Once arrived, you’ll be in China. You can leave the airport if you like, but I’m not sure how tight your domestic connection is. Also, Shanghai has two terminals. You may have to walk from one terminal to the other. It’s not arduous, but it adds time if necessary.
What’s your status with the airline? You can usually get in the short queue for boarding with the most basic status, unlike in the USA. If you have to check in again for the connection, you can get in the short line with status, too, and of course if you’re business class, you get in the short line, too. Desk agents all speak enough English in any line to get you booked.
If you have time, hop on the Maglev train. It’s about an eight minute ride. Hope off, buy a return ticket, and go back to the airport. If you get on it at the right time of day you’ll get up to 450 km/h on the ground, and you also have bragging rights to having actually been in Shanghai. If you have even more time and are adventurous, you’d only be a few subway stops from a good, Western, English-speaking shopping mall in Pudong (the part of Shanghai east of the Pu River, very modern).
Don’t be surprised if the taxi driver can’t read your Chinese address. I’ve had taxi drivers ask people what was written on my written instructions at times! If it’s a major hotel, try to use Google Translate to speak the Chinese pronunciation of your hotel, assuming it’s a large, prominent hotel. (Djo ji joe dian I still remember to this day).
In Wuhan my parting gift from WISCO was their local duck, mostly necks and skinny bits, so that’s probably the local delicacy. If offered any, be polite and try to nibble off the fleshy bits that you can. And if offered a parting gift, try to refuse it a couple of times, just to be polite.
Unfortunately I didn’t have a chance to see much of Wuhan that I wasn’t shown, so no specific Wuhan advice. On the other hand, as an honored guest, I expect that someone will invite you out to dinner every night that you’re there. Accept, and maybe you can get good suggestions/invitations from others there. And the Chinese business or “business” dinner experience is something that’s fun. It’s both formal and informal at the same time, and completely different from most American experiences.
Don’t forget: don’t worry in advance, take it in stride, and have fun and adventure!