@2008traveler:

Easy answers first! Athens is a very safe city, similar to every big city in Europe. Standard precautions should be taken, such as not having an easy to open bag in the metro during rush hour, etc., but other than that no problem for single females.

Now to the more difficult ones: What yopu can do in 10 hours depends on what you'd like to see. At the time you arrive, traffic should be light, so even if you take the bus (which personally prefer), you should be in the city centre (Syntagma square) in about 45-5- minutes, same time as by underground. Check its schedule, as it leaves every 30 minutes from the airport. At any rate, considering your trip into the city and the trip back, you're left with about 7 hours for your visit. I'd suggest the Acropolis Museum and a fast visit to the Acropolis proper, then walk down towards Monastiraki, make a short walk through Plaka (the old part of the city) and then take the train back to the airport. This way you'll get a pot-pourri of ancient, not so ancient and modern views of Athens and the noise that accompanies them. Careful, if its a sunny day get a bottle of water as it can get uncomfortable walking in the sun even in the winter. HAve a nice... day (literally!)