Don't let the "hostel" moniker fool you -- AthenStyle is very budget-friendly, but it also caters to those looking for a little more. I stayed in a beautiful suite here, complete with a small kitchen and a gorgeous stone balcony. Its location next to Monastiraki Square was perfect, as was its friendly staff.
I returned to this hostel time and time again on my travels. Its epic rooftop patio was a pretty key factor, thanks to its happy hour specials and the views of the Acropolis lit up in fully glory at night.