There are no shortage of options in central Athens ranging from backpackers' hostels to five-star historic buildings and contemporary cutting-edge boutique hotels.
As ever, the most important choice you will have to make comes down to location, location, location. With such a wide variety of options, it's best to focus on the area that you want to stay in (close to the sights, or a particular metro stop) and search for hotels in that area, because otherwise you'll be picking through hundreds of options all over town.
Most of the sights are within walking distance of each other, so central hotels will be best for most people (and also handy for the Metro). We would recommend looking for hotels on/around Syntagma Square, Plaka or Omonia Square. Naturally the best hotels located in these areas can be pretty pricey, but there are still budget options available.
Hotels.com and Booking.com are our recommendations for booking sites - be sure to check the location, though, or you could end up with a great deal on a room rate but end up out in the sticks and nowhere near a metro station. If you want to make sure that the place you're staying in is more like The Ritz than the pits, we'd advise a little trip to Tripadvisor, too, for some independent reviews.
Also, with these sites you are more likely to end up where you are booked, rather than at a smaller 'sister' hotel to the one indicated on other websites. Be wary of supplemental charges, too, as these can often be hefty.
If you're looking at the budget end of the spectrum, we heartily recommend Hostelbookers, whose reviews have proven time and again to be trustworthy.