Margaret Wade Labarge's book Mistress, Maids and Men (originally published as A Baronial Household of the Thirteenth Century) looks at English noble households by studying their accounting books. Here's what she had to say.
Some estimate of the average distance covered in a day by [a thirteenth-century English] household can be gained from the countess of Leicester’s account in February; when the household was at Wallingford, it moved on to Odiham by way of Reading, spending one night there. The journey on each of these days was just over fifteen miles, the normal pace of such a move in midwinter. But in June, when the countess had to hurry across country with her household to the greater safety of Dover castle, she consistently travelled thirty miles a day. This may reasonably be considered as fast as such a large company could move, and the sustained rate of speed hints at the urgency that drove them on.
All thirteenth-century travellers did not of course belong to large retinues, and small groups with good horses travelled much faster. The merchant could do between thirty-five and forty miles a day, travelling only in daylight hours, if his merchandise was light and easily carried on one horse. Freight services, such as commonly transported wine in England or travelled the alpine passes with goods from Italy for the fairs of Champagne, were among the slowest of all traffic. Fastest of all was the messenger, for he also travelled at night and often requisitioned extra horses along his route. He might cover as much as fifty-five to sixty miles a day. (pp. 156-7)
Peter Spufford, looking at late medieval merchants, mostly in continental Europe, comes up with very similar numbers. (Keep in mind that a mile is 1.61 km and a kilometer is 0.62 miles.)
The normal distance travelled by any type of carrier in one day seems to have been in the region of 30 to 40 km. The stages for pack animals over the Simplon pass were a little more than 30 km apart. ... Further along the route north, heavy four-wheeled carts on the roads between Salins and Paris also covered 30 or 40 km a day, although the lighter, shorter-distance, two-wheeled carts seem only to have been capable of covering under 30 km a day. If moderately loaded packhorses were used on these easier roads between Salins and Paris, as they sometimes were for special loads, they were able to travel longer distances, over 40 km a day. Indeed a convoy of four men and six horses did the journey from Dijon to Paris in six days in January 1412, averaging 50 km a day. ... The distances covered by non-commercial travellers were not very different from the normal speeds of carriers. Archbishop Eudes Rigaud and his retinue averaged 33 km (20 miles) a day between Paris and Dijon in 1254. In practice their day’s journey varied in length between 20 and 45 km, but the archbishop was taking it slowly, visiting friends and acquaintances all along the way. (p. 200)</i>
Drawing on the work of Italian historian Federico Melis, Spufford also discusses what we can discover by looking at the dates that letters were sent and received in late fourteenth and early fifteenth-century Italy. These sources tell us about the speed of messengers, who usually travelled lighter and faster than other people.
The 17,000 letters between Florence and Genoa normally took 5 to 7 days to deliver, as did the 7,000 letters between Florence and Venice. Outside northern Italy delivery times were not so consistent. The 13,000 letters between Barcelona and Valencia normally took between 3 and 6 days to arrive. If a greater distance was involved, including travel by boat, the times were even more variable. The 348 letters between London and Naples varied in delivery times from 27 to 75 days, although most arrived between 32 and 54 days after despatch. This should be compared to Uzzanno’s note that letters from Florence to London (over 1,500 km plus the Channel crossing) should take under 30 days. Real couriers could travel faster than expectations as well as a great deal slower. Water could be faster than land, for most of the 493 letters between Venice and Constantinople were delivered in 34 to 46 days. (p. 27)
In other words, speed depended on weather conditions, how much baggage you were carrying, and how much of a hurry you were in.