I'm going to be in Beijing for 8 days at the end of October. I'm trying to figure out how I should spend my time. I've never been to China (or the rest of Asia) before.

My girlfriend points out that I speak no Chinese of any sort, and all the guided tours and touristy spots seem "doable" in 4 days, including the Great Wall, so she thinks I'll get bored if I stay 8 days, and I should head to some other Asian city for part of my stay. I could do that, but my departing flight has to leave from Beijing, and I don't want to spend more than $400 leaving Beijing and coming back.