If you try Jerusalem artichoke (aka sunchoke), I highly recommend a large pot. They grow from tubers like potatoes, and are native to the U.S. If you miss even one tuber during harvest, you will have a large plot of them pop up the next spring. Which is great, unless you wanted to grow something else in that spot!
I want to try galangal this year (aka thai ginger). Bought a promising piece at the market thats already sprouted from a few different eyes, but not sure if it could potentially take over in my zone or not...gotta check before I plant.
Also, turmeric. You can find the roots at many of the "fancy" grocery stores or farmers markets.