The bombing of Brooklands was comparatively minor, but to facilitate entry and exit there were two breaches cut in the banking, as well as several buildings being constructed around the course. In a way Brooklands was lucky, in that it was very effectively camouflaged to resemble a housing estate - there were also some similarly shaped reservoirs nearby which confused attacking bombers and on several occasions they actually bombed those; they also hit the adjacent railway line. There are descriptions of several Brooklands raids in a book called 'Raiders Overhead: The Bombing of Walton and Weybridge' by Stephen Flower (Air Research Publications, Walton-on-Thames, 1994). Google Earth has a 1945 or 1946 aerial photograph which is very revealing, as it was taken after the camouflage had been removed; it was discovered that some of the unseasoned poles which had held it up had apparently taken root, which didn't do the surface much good.
Part of the Clady public road circuit in Northern Ireland was obliterated by a wartime airfield.
As LittleChris says, Donington Park was a military facility. The pits, grandstands and spectator bridges were all wooden constructions and dismantled early in the war and the wood reused elsewhere. The army built a lot of temporary structures and several new roads on the site and apparently kept the circuit itself in a decent state of repair.
Crystal Palace was a mess by the end of the war - it had first been used as an internment camp for Axis merchant seamen detained in British ports and then - after Dunkirk - as a refugee camp. From mid-1943 it was a breaker's yard for scrapped government-owned vehicles, so as you might imagine it wasn't exactly pristine when handed back in 1945.
As far as I'm aware most of the damage to Monza was caused by the US Army, who used it as a transport depot, as well as for a big victory parade. This is the South African 6th Armoured Division during that parade - General Mark Clark is up on the podium taking the salute.
Montlhéry was also used by the Americans, although it was already in a bad state of repair when they arrived in 1944. Earlier it had been used as a prison camp for Tsiganes and - before the fall of France - as a training centre for French motorcycle troops.
I think I've seen a reference to the Wehrmacht using parts of the Nürburgring for tank testing and - again - the US Army used it in various ways, not least because the local roads were badly damaged and lined with wrecked vehicles. Reputedly quite a lot of documents, photos etc 'went missing' while the US Army were in occupation and several buildings burned down.
