If you commit a crime in unclaimed territory, where do you get tried?

Well in maritime/admiralty law, they will often go by the nationality of the vessel, so if any dispute over jurisdiction, if something happens in international waters, or when the ship is otherwise not sailing in areas that some other nation can exercise jurisdiction, they go by its registered flag state. If no registered flag or nationality of the vessel is able to be established, then it would go by its last port of call.

So in your moon example, probably whichever country his space ship took him to the moon on or where the spaceship was registered at. If no spaceship flag registration, and built by a bunch of space pirates or something, then would likely go by space ship's last port of call, so unless the space ship first stopped off on another planet that had its own justice system, wanting to exercise jurisdiction over the case, it would have had to come from a place on earth, and it would be the country on earth where the space ship launched from.

So probably US, Russia or China, as we're the only three countries on earth who have done space launches.

However, like the other poster said, if modeled after the Antarctica Treaty, then could be different if there was such a treaty in effect at the time. Otherwise it would likely default to the old maritime/admiralty laws, which some laws go back over a thousand years. Literally. Because for over a thousand years, we've been sailing the earth and bad stuff happens sometimes out in the middle of the ocean, and we've had to come up with ways to deal with them.

She get's tried in her country of residence

Astronauts remain under the authority of the country who employs them..... but as the US must rely on the Russians for transport and landing.... it is very likely.. if a major crime were committed by an American... that the trial would be in Russia... depending on what international agreements have been made

According to NASA she will be tried in the country of her nationality.

Carol is right. My guess is that the "crime" was actually committed at the point of the bank account, and that state would have jurisdiction. But this will be interesting to watch.
Yes, of course someone who commits murder on the moon- or, more realistically, on a space station, would be tried. But there would be lots of jurisdictional rulings.

Yes, they can be tried, but it may end up in the international court at the Hague in Brussels. There have been incidents in Antarctica, including an attempted murder. The 1967 U.N. Outer Space Treaty was modeled after the Antarctica treaties.

What was the nationality of the person who hacked into his ex's bank account? It probably would not get any higher than the state / province level.