My wife has a client for whom she did some DNA research (using the client's DNA of course). The only things that were commercially available to the public/my wife provided information on the "proclivity" towards certain illnesses. Your DNA won't show nationality, although if certain things show up, like the person is a Tay-Sachs carrier, then it is not unreasonable to conclude that somewhere, someone was of Eastern European Jewish origin.
Overall, the client was not that impressed with the results. On the other hand, if you have access to law enforcement databases or something similar, you might get more detailed feedback.