The Dead Rat Tavern
The original owner of the Dead Rat Tavern, a seedy joint down by the docks, was not the wisest of men, and stiffing a sorcerer half his fee for brewing a dozen barrels of illegal Liquid Fire is a classic example something only an idiot would do. Nobody was surprised when a string of bad luck ended with the tavern burning down, and the owner being arrested less than a week later. What has surprised many is the original owner's nephew re-opening the tavern in various locations around the city. The word various is used since the sorcerer's curse seems to still have plenty of juice in it, causing the tavern to be spectacularly destroyed on a regular basis. Why the new owner doesn't just walk away from the establishment is a mystery.
The Adventurer's Guild
The previous PyresBaron founded the official Adventurer's Guild in an attempt to rest taxes from the heavily-armed vagabonds that frequent the city. The project was a complete failure, as the city's adventuring population, while small and usually quite fractious, banded together in their utter refusal to band together. Now the small but rather grandiose building sits and molders, its windows boarded up and doors locked.
The Pyresburg Zoo.
The zoo has a long history in Pyresburg. It started out as a facility to house creatures used for fighting in the Arena, but was later expanded to house the private menagerie of one of the Pyresbarons. When the Arena was burnt down in the great fire, the Zoo miraculously survived, and shifted its focus to showing its exotic animal collection to the public.
Pyresburg Academy of Magic
Originally the Academy was one of the best on the Coin, famous the world over for producing wizards of the highest caliber, especially in the field of fire magic. Sadly, about 20 years ago, the Academy buildings exploded in a fireball of horrendous proportions, causing the great fire. When the fire was put out, the only surviving wizards were the handful of students and staff who had been elsewhere at the time. This handful were tasked with rebuilding the institution, no easy task after the loss of hundreds of years of accumulated magical works. Now the Academy has a more reasonably sized staff and a sizable student body, but they're desperate for additions to their library. PCs with looted books, or a new spell they've found or developed could do well visiting the new Academy.
The ground under Pyresburg has more air in it than an Orzorvian Cheese. Basements (including those of the destroyed university), sewers, crypts, smugglers' tunnels, dwarf squats all jumble together under the streets. Many valuable things are lost, or appear, in the undercity, but many unpleasant things frequent the darkness down there as well...
A 25-foot-wide, 120-foot tall solid tower topped with a great fire, the Pyre for which the city is named has stood on its small rocky spit, serving as a lighthouse for as long as recorded history. In times of danger it is also used as a signal to the surrounding countryside by the simple expedient of adding an alchemical agent to change the colour of the flame.