Yes, in fact the two big crusades of the 13th century were directed against Egypt, the Fifth Crusade in 1217 and Louis IX’s crusade (or the Seventh Crusade) in 1249. The Fourth Crusade in 1202, which ended up conquering Constantinople, was originally intended for Egypt as well.
During the 12th century, Egypt was one of the crusaders’ most powerful enemies. During the First Crusade, Egypt was ruled by the Fatimid dynasty, and Syria was ruled by various Seljuk Turkic states. The Seljuks and the Fatimids were enemies, partly because they followed different forms of Islam - the Fatimids were Shia and the Seljuks were Sunni. They were still. fighting each other when the crusade arrived. Jerusalem actually passed back and forth between the Seljuks and Fatimids while the crusade was marching there. In July of 1099, the crusaders captured it from the Fatimids. The crusade is often considered to have ended a month later, in August, when they defeated the Fatimid army that had been sent from Egypt to relieve Jerusalem.
That battle took place at Ashkelon, which remained an Egyptian stronghold right on the doorstep of the crusader Kingdom of Jerusalem for over 50 years. Fatimid Egypt remained one of Jerusalem’s major enemies, and new waves of crusaders from Europe fought battles against the Fatimids in 1101, 1102, and. 1104. In 1118, King Baldwin I of Jerusalem tried to invade Egypt but died of an illness while he was there. The Fatimids invaded Jerusalem in 1123 but the crusaders defeated them, and finally in 1153 the crusaders captured Ashkelon, which (for the most part) eliminated Egypt as a threat.
However, they could easily see that controlling Egypt was important for controlling the Levant. Further to the east, the crusaders’ other enemies in Syria could also understand that. By this time, Syria was mostly united under the Zengid dynasty. In the 1160s and 1170s, both the crusaders and the Zengids tried to conquer Egypt at the same time, and the Fatimids sometimes allied with the crusaders against the Zengids, and sometimes with the Zengids against the crusaders…it’s very confusing, but in the end, one of the Zengid generals, Saladin, managed to overthrow the Fatimids and defeat the crusaders. Since Saladin wasn’t technically a member of the Zengid dynasty, we call his own the dynasty the Ayyubid dynasty after his own family (sorry for all the names, I hope this makes sense!).
Saladin also inherited or conquered all of the Zengid territories in Syria, so he ended up surrounding the crusaders, and he recaptured Jerusalem in 1187. So the crusaders understood very well how important Egypt was. In t he 13th century, Egypt became the focus of their strategy to take back Jerusalem. As I mentioned above, the Fourth Crusade in 1202 was originally intended to attack Egypt, before it was diverted to the Byzantine Empire.
The Fifth Crusade in 1217 also sailed for Egypt. Alexandria was important (see below), but since it’s on the western side of the Nile Delta, they decided to attack Damietta instead, which is on the eastern side of the delta and closer to Jerusalem. And it worked, at first! The Fifth Crusade captured Damietta briefly, but the crusade was defeated when the Ayyubid sultan of Egypt destroyed the dams on the Nile, so the crusaders were flooded out of the city and were defeated.
The next crusade, by Holy Roman Emperor Frederick II, sometimes labelled the Sixth Crusade, managed to regain Jerusalem, but by peace treaty rather than by force. Frederick realized that it was actually pointless to attack Egypt, but he got Jerusalem back by negotiating with the sultan of Egypt instead, in 1229. So the crusaders held Jerusalem again until 1244, but it wasn’t totally peaceful, because the various branches of the Ayyubid dynasty in Egypt and Syria were always at war with each other, and with the remaining crusaders in the Levant, so Jerusalem passed back and forth between them sometimes. The treaty between Frederick and the sultan only lasted for 10 years until 1239, and in 1244 the crusaders lost Jerusalem again for good.
The crusade of Louis IX (or sometimes the Seventh Crusade) also attacked Egypt, and just like during the Fifth Crusade, they managed to capture Damietta briefly. But Louis was defeated and imprisoned by the Ayyubids in Cairo. Thanks to the pressure of the crusade, and the apparent weakness of the Ayyubid rulers, the Ayyubid army of slave-soldiers revolted and overthrew the Ayyubid dynasty. The soldiers, the Mamluks, established their own dynasty, which ruled Egypt for over 300 years. It’s always amazing to me that the Mamluk revolution happened in the middle of the crusade! Louis IX was watching it happen from his prison cell.
That was the last time a crusade tried to conquer Egypt, and the Egyptian Mamluks eventually destroyed the Ayyubids in Syria as well, and by 1291 they had conquered all the remaining crusader cities in the Levant too. In the 14th century, there were plans to invade Egypt again, but nothing happened because everyone realized how futile it was.
As for Alexandria and Cairo specifically, well Cairo was a target simply because it was the capital of Fatimid, Ayyubid, and Mamluk Egypt. It didn’t have any religious significance for Christians, but they would have to control if if they wanted to control Egypt.
Alexandria wasn’t usually a target, but it was definitely important, religiously speaking. It was one of the 5 ancient patriarchates of the church, along with Jerusalem, Antioch, Constantinople and Rome. The church there was supposed to have been founded by St. Mark, so it was one of the oldest Christian cities and it’s still an important Christian city in modern Egypt. There were Greek and Coptic patriarchs there at the time of the crusades, and there was even a titular Latin patriarch. That title was created in the 13th century in preparation for the Fifth Crusade, just in case the crusade worked and they actually occupied Alexandria. No Latin patriarch ever resided there, but the title continued to be used up to the 20th century!
So, there were many crusades against Egypt, since Egypt was probably the most significant enemy of the crusades. Alexandria wasn’t specifically targeted, although it was a very important city in Christian history and they hoped to regain it along with the rest of Egypt.
Sources:
Any good history of the crusades will discuss the importance of Egypt. Personally I like Jonathan Riley-Smith, The Crusades: A History, 3rd ed. (Bloomsbury, 2014)
There is also an excellent history of the Fifth Crusade, which talks about how Egypt became a target: James M. Powell, Anatomy of a Crusade: 1213-1221 (University of Pennsylvania Press, 1986)