What was destroyed:
Two stone gargoyles:
“The first casualties of the battle were already strewn across the passage ahead: the two stone gargoyles that usually guarded the entrance to the staff room had been smashed apart by a jinx that had sailed through another broken window. Their remains stirred feebly on the floor, and as Harry leapt over one of their disembodied heads it moaned faintly, ‘Oh, don’t mind me … I’ll just lie here and crumble …”
“As they reached the end of this corridor, the whole castle shook and Harry knew, as a gigantic vase blew off its plinth with explosive force, that it was in the grip of enchantments more sinister than those of the teachers and the Order.”
A statue (possibly on purpose):
“Harry hurtled round a corner and found Fred and a small knot of students, including Lee Jordan and Hannah Abbott, standing beside another empty plinth, whose statue had concealed a secret passageway.”
Another stone gargoyle:
“Looking down, Harry saw Grawp the giant meandering past, swinging what looked like a stone gargoyle torn from the roof and roaring his displeasure.”
“As long as it’s not any of our lot!’ said a voice: Harry turned and saw Ginny and Tonks, both with their wands drawn at the next window, which was missing several panes.”
The objects in the Room of Requirement:
“The door, get to the door, the door!’ screamed Malfoy in Harry’s ear, and Harry sped up, following Ron, Hermione and Goyle through the billowing black smoke, hardly able to breathe: and all around them the last few objects unburned by the devouring flames were flung into the air, as the creatures of the cursed fire cast them high in celebration: cups and shields, a sparkling necklace and an old, discoloured tiara –”
Possibly, but not certainly, the Room of Requirement itself:
“Where’s Ginny?’ he said sharply. ‘She was here. She was supposed to be going back into the Room of Requirement.’
‘Blimey, d’you reckon it’ll still work after that fire?’ asked Ron, but he, too, got to his feet, rubbing his chest and looking left and right.”
A wall at the side of Hogwarts:
“And then the world resolved itself into pain and semi-darkness: he was half-buried in the wreckage of a corridor that had been subjected to a terrible attack: cold air told him that the side of the castle had been blown away and hot stickiness on his cheek told him that he was bleeding copiously.”
Masonry and the glass from the windows:
“Malfoy and Goyle had vanished, but at the end of the corridor, which was now full of dust and falling masonry, glass long gone from the windows, he saw many people running backwards and forwards, whether friends or foes he could not tell.”
“Before Hermione could get further than, ‘Ron, I’m just as capable –’ the tapestry at the top of the staircase on which they stood was ripped open.”
Stone from an unmentioned location:
“But he threw it over all three of them; large though they were, he doubted anyone would see their disembodied feet through the dust that clogged the air, the falling stone, the shimmer of spells.”
The hourglass counting Slytherin’s house points:
“Harry, Ron and Hermione sped down the marble staircase: glass shattered to their left and the Slytherin hourglass that had recorded house points spilled its emeralds everywhere, so that people slipped and staggered as they ran.”
“And with a movement like a tennis serve, she heaved another enormous crystal sphere from her bag, waved her wand through the air, and caused the ball to speed across the hall and smash through a window.”
Yet another window:
“With one brutal, fluid movement, it smashed a massive fist through an upper window and glass rained down upon Harry, forcing him back under the shelter of the doorway.”
The door leading to the Hogwarts kitchens:
“The centaurs Bane, Ronan and Magorian burst into the Hall with a great clatter of hooves, as behind Harry the door that led to the kitchens was blasted off its hinges.”
Bonus - before the battle officially began:
A suit of armor:
“Flitwick’s spell hit the suit of armour behind which Snape had taken shelter: with a clatter it came to life. Snape struggled free of the crushing arms and sent it flying back towards his attackers: Harry and Luna had to dive sideways to avoid it as it smashed into the wall and shattered.”
“Harry dragged her to her feet and they raced along the corridor, trailing the Invisibility Cloak behind them, into the deserted classroom where Professors McGonagall, Flitwick and Sprout were standing at a smashed window.”
Was anything permanently destroyed?
The only things that are certain to be permanently destroyed would be the items in the Room of Requirement. Fiendfyre is known to put objects beyond magical repair - which is why it can be used to destroy Horcruxes. It’s most likely very difficult to put an object (rather than a person) beyond magical repair, since there are very few things known to destroy Horcruxes, and putting them beyond magical repair is what’s needed to destroy them. It seems very likely that nearly everything in Hogwarts could be fixed or replaced.
The Sorting Hat was not permanently destroyed.
Harry tells his son in the epilogue that the Sorting Hat would consider his opinion, meaning it’s very likely the same Hat that Sorted Harry.
Hogwarts becomes a usable school again.
As we see in the epilogue, Harry and his friends’ children attend Hogwarts, so it was certainly fixed back into a working school.