Most areas in Athens are safe for walking even in late hours.   A good place to stay is around Syntagma Square where everything is in close distance - restaurants, cafés, shops, and ancient sites.  Also recommended are Ilysia, Vas.Sofias and Panepistimiou Street.  Here there are many hotels, restaurants and taverns. 

** Note:  The original information for this thread came from the following forum thread: