According to travel experts, trips to Greece are currently safe. An article from MSNBC reports:
The most important thing to realize is that the riots, which led to dozens of looted shops and buildings lit afire, have been located in the downtown core, specifically Syntagma Square, said Rich Sorensen, travel news editor for Europe Through the Back Door in Edmonds, Wash. The riots were touched off by the Greek government’s consideration of tough austerity measures to deal with its ongoing debt crisis. The government approved those measures Monday.
It’s important to remember that riots and civil unrest are not covered by most travel insurance policies. In the event someone planed a trip to Greece, and they no longer wanted to take that trip, they would need to have a travel insurance policy with Cancel For Any Reason. Cancel For Any Reason would allow them to cancel their trip without an explanation. Unlike Trip Cancellation coverage, they will only receive up 75% of their trip cost and must cancel prior to 48 hours of their departure.
Always refer to the certificate of insurance for details.