Because Greece is a touring area, there are many hotels whit a different stars and different prices. The personal of the hotels are very hospitable behave very careful with their clients.
Since i also got the Greek Citizenship there are many hotels that you can find, not in such affortable prices for the US Citizens(anymore) because Greece uses the Euro Currency.
You can find both in the center of Athens and in the rich suberbs of Athens like Marousi, Kifissia, Ampelogarden, Peristeri, Pireus and more.
I went to Greece last years. It was very nice country city. I stayed One 5 star hotel the name was Hotel Grande Bretagne In Athens. It was awesome hotels really the hotels facility was very nice and also hotel staff. I really very much enjoyed there.Ideally located within short walking distance of exclusive shopping areas, restaurants, open-air cafes, museums and the business district