For big cities, I wouldn't worry about the "touristy" problem. You learn where those areas are, then avoid them. There's always a Real China neighbourhood nearby, if you take the time to find them.
The "tropical/subtropical" definition is a tricky one. Suzhou, not far from Shanghai, is certainly tropical in the summer; I grouse on about it for 5 months of the year. It frequently hits 40C with a jillion percent humidity. But right now it's near freezing, with a damp, biting wind. Spring and Autumn are paradise, but you get extremes here otherwise. China's like that.
Whip out a map and use Shanghai as a standard. Frankly, too hot for me- if Suzhou wasn't my true love, I'd move North.
By "hardcore", I mean a rural locale where nobody speaks English and women still wash clothes by the well. I had that for my first year, and I wouldn't trade the experience for anything- but I'll be damned if I'll do it again. The other extreme would be Beijing or Shanghai, aggressively modernized metropoli.
Followup questions?