You didn't say when you would be there . . . that could help with suggestions. Also your budget.
We always stay at the Attalos Hotel on Athinas St., one of the best budget accommodations in Athens with a wonderful rooftop garden/bar with spectacular views of the Acropolis and the rest of Athens.
As a backup I would suggest Hotel Cecil, just up the street from the Attalos. A little below the Attalos for quality but still fine. It's cheaper and the price includes breakfast whereas the Attalos charges for their breakfast.
I'm sure there are a number of other accommodations that are good but the above two are my to-go-to hotels when in Athens.
And I also agree that it's best to deal directly with the hotel rather than a third-party agent. You'll probably get a better deal and customer service.