Steve,
I worked in Athens for a summer, so I managed to make my way around the city. I would avoid hotels near the city centre. The Hilton and Intercontinental are near shopping and restaurants, safe, less touristy, and near the subway. The Crown Plaza isn't near much shopping, but the area is safe, near some tavernas, and the subway. Any hotel in the Plaka should be safe, but restaurants and shopping are tourist-oriented. I cannot comment on how reasonable the prices are. If price wasn't an issue, I would shoot for the Grand Bretagne; it's across from Syntagma square from where it's easy to catch a train anywhere else. I liked the Hilton location; it's close to restaurants and shopping that the locals would frequent. It's also a nice (but uphill) walk past the British embassy up to Lycabettus Hill, which offers a great overlook of the city (especially at dusk).
Good luck,
Mark