If you have the time and means I would suggest hiking the unrenovated part of the Great Wall. It sounds like you're an accomplished hiker so it will not be a problem for you, and will be MUCH less crowded than the touristy part of the Great Wall.
It's best as a one-way hike so you arrange to have a car pick you up at the end of your hike. We hiked a section and it took us 4-5 hours moving at a very slow pace (one of my friends is a chain smoker). The unrenovated part has some parts where you walk over crumbling parts of the wall and others where you will have to dismount from the wall but it's nothing super technical.
Be forewarned that there are admission fees in the middle of certain routes on the unrenovated part so bring some cash. Also, there will be hawkers trying to sell you stuff ... and in some cases they will follow you until you buy something (and even after you buy something). One group of hawkers followed us for two hours (not an exaggeration) and only left us when we hit a "toll booth". If you are easy to peg as a Yanqui (as we were), you're likely not to escape this sort of treatment; nothing like being harassed while you're on vacation.
For Xian I would also recommend seeing some of the lesser known burial mounds. They also have terra cotta warrior displays but on a much smaller scale. It seems after the main cache was created, subsequent rulers didn't have the budget to do the same thing so they buried smaller armies of smaller statues (some no bigger than six inches tall). Again, these are less crowded than the main warrior exhibit and very interesting to boot.
I don't have much to add on Shanghai itself. The touristy stuff isn't half bad. We took a ride up the Pearl Tower and also got on a sunset cruise down the river.
If you have an unlocked quad band GSM cell phone you can buy a prepaid SIM card for your mobile phone needs. Note that it's not as easy as buying a SIM card in Europe; you'll have to fill out some forms in order to buy one. I don't read or write Chinese so I had my buddy from Shanghai fill them out for me. In any event, it's worth the time to buy a SIM card, otherwise you'll be paying outrageous international roaming rates.
Hope you have a great trip!
