However, citizens of the United States and Canada can discount this option altogether (and don't bother with the Disney castles either). Since the founding of both these countries, the rise of firearm warfare, and explosives made traditional defenses like castles obsolete, so they are in short supply, though there are several.
One should also know the fundamental difference between a castle and a palace. A castle is a fortress, with large physical barriers designed to keep out hordes of enemy soldiers; A palace is little more than a fancy home, with large open windows and doors, simple iron bar fences, and open verandas purely for aesthetic purposes. Hiding from a zombie horde inside a palace will get you and yours killed faster than you can say "Let them eat flesh!" In the novel World War Z, there is a great contrast depicted: Windsor Castle became the most successful fortress in England during the zombie war, if not Europe; In stark contrast to this is France's Palace of Versailles, upon the ashes of which the French put their national monument.
One should also know the condition of the castle you plan to inhabit, since many have been neglected, damaged, or altered to increase their aesthetic value once the rules of European warfare changed from melee combat to firearms. Also, as with any base, you'll have far more threats than simply the undead to worry about. Food, water, ammo, medicine, morale, illness, and insurrection are all major problems you'll likely have to deal with during the long haul. If you're in a castle above the snow line, than take the opportunity to use the winter months to raid the surrounding countryside for supplies, check your defense from the outside, and even bash the heads of your attackers while they're frozen solid.
The castle is a great option for survivors, or those trying to survive, in Europe, especially England and Scotland, and to a larger extent, Wales. Wales is often called "the castle capital of the world". It has 100 castles which still stand. The English Heritage and the Natural Trust both maintain historic buildings such as castles. If you can get to a restored castle, do so but be careful as most castles were destroyed during and after the English civil war, though this only applies to England. It's likely they'll have some food supplies (albeit not enough for a siege ironically) so bring your own. Also bring your own weapons; the weapons the previous defenders used will be located in the museum, often some distance away. Ranged weapons are preferable, although they'll most likely be makeshift although local police do have small stocks of firearms but nowhere near the quantity of a gun store in the USA.