I'd echo the general thrust of the posts so far - a few things that are worth seeing; a couple of major problems (smog!); overall, I'm not sure it's worth a special trip. Japan though - now that's worth a special trip...
I've been several times, I quite like Beijing but prefer Shanghai and love Hong Kong. If you get the chance Yangshuo/Guilin are great places to kick back for a few days, and only an overnight train journey from Beijing. Xi'an on the other hand is an absolute waste of time IMO. I found it really overrated, it's miles from anywhere and other than the Terracotta warriors there's nothing there.
Travelled in China for 3 months a while ago. The highlight was Tibet - and October/November is a perfect time to go - clear skies over the Himalayas. You'd need about 10 days and depending upon the tour you take, it might end up in Kathmandu and you could easily spend a week in Nepal (and in fact you could do a trek there if you are into that sort of thing - I walked to Everest Base Camp at Xmas - fantastic, takes 2 weeks). Loved Sichuan Province just east of Tibet as well. No trip to China is complete without a few days in Beijing as well - despite the pollution.
Taiwan is beautiful, and largely bypassed.
A lot of what China has on a smaller scale, few tourist hoards outside of holidays and weekends
Got a chance to sample downtown Taipei. Which was nice.
Besides the National Palace Museum and the Chiang-Kai Shek memorial, downtown Taipei appeared to consist of almost nothing but cake shops and wedding outfitters when I was there.
I've heard about the spitting thing, and I'm well aware of the pollution, yeah.
Would look to travel around a bit rather than stay in one place. Got to do Beijing I think just to see the Great Wall, but other than that, various people have suggested they enjoyed Shanghai (and Hong Kong) more.
Thanks
Giving it some thought for a holiday, say October or November time. It does look like an interesting sort of place.
Anybody been? Would you recommend it? Can't recall if we have a Seagulls Over Beijing branch