The Klingon First City in 2366. The Great Hall is visible on the left, the Old Quarter can be seen on the right
The First City of the Klingon Empire was located on Qo'noS and was the location of the Great Hall, where the Klingon High Council met.
The city itself is divided into quarters, one of which is the Old Quarter, where Kahlest resided in 2366. (TNG: "Sins of the Father") The House of Duras resided within the city. (TNG: "Redemption") The House of Kozak had its ancestral home within the city. (DS9: "The House of Quark")
The skyline of the First City was a matte painting created by Illusion Arts. (Star Trek Encyclopedia)
"Looking for par'Mach in All the Wrong Places" implies that "a Great Hall" was located in Qam-Chee, which may be the Klingon name for this city. The episode may be referring to a different Great Hall, though.