Tourism certainly existed - people travelled to other parts of the world to see the sights, there were hotels, and tour guides, and guidebooks, and tourists left accounts about what they saw. But pre-modern tourism was almost always a religious pilgrimage. I suppose we distinguish tourism from pilgrimage these days, but they’re very similar even today.

For example, one popular pilgrimage spot was Rome - just as it was on the “Grand Tour” in the 18th/19th century. Medieval people certainly knew about the old Roman Empire and the importance of Rome as a city. In the Middle Ages it was relatively small, but it was where the Pope lived (well...usually), so it was still politically and religiously important. Maybe less attention was paid to the old Roman sites, but it was also full of churches and cemeteries and other Christian pilgrimage sites.

Visitors were mostly religious pilgrims on their way to the various churches associated with the early Catholic saints and martyrs. Most importantly, Sts. Peter and Paul were believed to be buried there. Today, St. Peter's Basilica in the Vatican is one of the biggest churches in the world, and the same was true back then, although it was a different building. The first basilica was built all the way back in the 4th century, and lasted until the new one was built in the 16th century. It was full of burial sites and statues and mosaics.

Pilgrims sometimes left descriptions of what they saw in Rome, such as the Notitia ecclesiarum urbis Romae (a "list of churches of the city of Rome") and De locis sanctis martyrum ("on the holy sites of the martyrs"). There is one by "Master Gregorius" who saw the the Forum, and the Colosseum. He saw art such as a statue of Venus, and a statue of the wolf suckling Romulus and Remus (although whether this was the same statue that is currently in the Capitoline Museums is the subject of debate...). Another account is the Mirabilia Urbis Romae by Benedict of San Pietro, which includes the Pantheon, the “memorial of the emperor Hadrian”, the “winding pillar of Trajan”, the “Colossean Amphitheatre”, etc.

Rome was pretty good but the place every pilgrim wanted to go to, if they could, was Jerusalem. Even during the crusades, when Jerusalem was briefly under Christian control again, it was far away and hard to get to, but lots of pilgrims did go all the way and some of them left accounts of what they saw there. The pilgrimage sites there were already well known because there are Christian pilgrimage accounts going back to the 4th century, for example. Under the crusaders, some sites were renovated and restored, especially the Church of the Holy Sepulchre, which was built in the 1140s-1150s. The crusades were originally described as a sort of armed pilgrimage, and visiting the Holy Sepulchre was the goal of every crusader - then their vow was considered to be fulfilled and they could go home again.

The Church of the Nativity in Bethlehem and the monasteries at the Mount of Olives and Mount Zion were also significant pilgrimage sites, as were Nazareth, the Dead Sea, the Jordan River, the Sea of Galilee, etc etc…sometimes the pilgrimage sites were also important to Jewish and Muslim pilgrims, like the Cave of the Patriarchs in Hebron.

There were other major pilgrimage sites in Europe. One is Santiago de Compostela, which is claimed to the burial site of St. James, one of Jesus’ disciples. In the Middle Ages, and today, there was a network of roads leading pilgrims to Santiago. Pilgrims would wear an image of a clam shell on the clothes and there were inns and hotels along the route. Even now, people still recreate the medieval pilgrimage by walking the entire route (I have a friend who just did this last year).

Another famous pilgrimage site was Canterbury, after the murder of the archbishop, Thomas Becket. People began visiting the site of his murder in the cathedral and miracles were reported, so it quickly became the most important destination for English pilgrims, but pilgrims from the continent came to visit it as well. Chaucer’s Canterbury Tales is about a group of pilgrims on the road to Canterbury.

You could go on a pilgrimage anywhere, really. You could go visit any sort of holy relic, and local churches liked to collect relics of saints so people would visit them. In Paris, King Louis IX bought a bunch of relics from Constantinople, including Jesus’ crown of thorns, and built a new church to house them (the Saint-Chapelle). Smaller churches might have the relics of saints of local significance; for example, I used to live in Nantes in France, where you can visit the relics of local Roman martyrs St. Donatian and St. Rogatian.

There were also travelling Islamic and Jewish pilgrims. Muslim pilgrims of course went on the hajj to Mecca but they could travel around to other places along the way. There were special groups to help organize a hajj, specific routes to follow, and other holy sites to visit along the way. It wasn’t too much different from the pilgrimage to Compostela. Ibn Jubayr, for example, travelled from Spain all around the Mediterranean, and Ibn Battuta travelled even further, all around Europe and Africa as well. Benjamin of Tudela and Petachiah of Regensburg visited the Jewish holy sites in the Near East, which were mostly under crusader control at that point. Benjamin even reports that at the Cave of the Patriarchs, mentioned above, the crusaders built their own shrine, but Jewish pilgrims could pay a fee and see the real site.

So people didn’t really travel just to go sit on a beach somewhere, and they weren’t going to visit a museum or a castle or anything like that, but they did travel on pilgrimages to see religious sites and relics. There were organized trips, tour guides, hotels, things people wore to distinguish themselves as pilgrims, different places competed with each other to draw in more pilgrims, maybe a bit of unscrupulous trade in relics, claims about how and why a site was holy and worth visiting, and sometimes people wrote about where they went and what they saw…seems a lot like modern tourism!

Sources:

Adrian J. Boas, Jerusalem in the Time of the Crusades: Society, Landscape and Art in the Holy City under Frankish Rule (Routledge, 2001)

Robert Bork, ed., The Art, Science, and Technology of Medieval Travel (Ashgate, 2008)

Norbert Ohler, The Medieval Traveller, trans. Caroline Hillier (Boydell & Brewer, 2010)

Margaret Wade Labarge, Medieval Travellers (Hamish Hamilton, 1982)

Anthony Bale and Sebastian Sobecki, eds., Medieval English Travel: A Critical Anthology (Oxford University Press, 2019)

Debra J. Birch, Pilgrimage to Rome in the Middle Ages: Continuity and Change (Boydell, 1998)

Also, here are a couple of older answers I wrote about pilgrimages to Rome and Jerusalem:

How did medieval travellers perceive Rome as a city?

What was Crusader ‘Tourism” like? Where the knights and lords who participated ever in much danger, or was it more fixed and showy like much Tourism today?