Tourism (as opposed to simple religious pilgrimage) did exist, though they didn't describe it as such. English, French and German nobles would travel to the Baltics with their retinues to help kill pagans, and then go back home. But...

The distances involved and the general similarity of wildlife across Europe, however, would have made hunting across the continent an unusual past time. Unicorns were not portrayed in the medieval popular mind as something distant, just as very rare. (Odell Shepherd)

Most of the megafauna living within reach of the average European nobleman would have gone extinct in the Roman Empire. Travel through Muslim North Africa and then the Sahara was so rare that I actually can't think of any westerner who made the journey until the Renaissance. India was slightly easier, as the land route was more hospitable, but the political climate in Persia and the Levant was hostile and it would have been quite expensive.

Western Europeans hunted boars and stags as a preference, and those would have provided great challenge for hunters armed with bows and spears. The last European 'exotic' (so to speak) would have been the auroch, which was well on its way out by the late middle ages. A historian of Poland would be able to answer the question of whether German or French nobles ever came to the Polish hunting parks to try their luck against these beasts.