I am going home for a couple months in the summer, and I want to bring some souvenirs as gifts. It doesn't matter if they are cheap for expensive. I will add my ideas below.
Money works well; I'm bringing home a handful of Chinese and HK coins and bills.
Some purses and random things I bartered for in HK.
A few free, Chinese-produced, English newspapers from USTC.
Several Chinese books for kids from street vendors, and also some neat notebooks for children from Walmart.
I might also get some cheap replicas of famous brands if I see them.
Also, last time I went home I brought a Chinese tea-set (a bit touristy) with some figurines that change color with hot water. It looked nice, but it has so many small fragile parts and takes up too much space.
So, yeah, add your ideas for souvenirs or gifts!