Back in the Middle Ages, travel was all on foot, be they your own, or a horse's. Thus it would all be about the same speed (3-4mph typically). Travellers would want somewhere safe to sleep at night, and villages could only really lay claim to land somewhat less than half a day's walk of it (less than half a day there, do some work, less than half a day back home), meaning that the nearest settlements were all approximately one day's walk away from each other.
At 3.5mph, walking for 8 hours, that would mean you'd come across a village every 28 miles. The original definition of a town was a settlement that had a weekly market. Thus most villagers would go to town to trade for what ever they can't produce at home. Thus towns would have to be close enough that villagers weren't travelling too far. Typically, this would mean that towns would be about three days away from one another (with the two intervening nights being at villages), with the nearest villages each coming to the town for trade.
Cities, being one step up from towns, would be the source of products that were unavailable in your local town. They would typically be just over a week travel from one another, with two towns and six villages between them.
This is all very subjective to geography however. Highly fertile lands means that settlements could be closer together, infertile lands, means they are further apart. Rivers were a faster means of travel and a source of water, so settlements tend to grow around them.
This fact can actually be observed when comparing the United Kingdom, which is riddled with tiny villages, and the United States, which has settlements much further apart, due to a day's travel being a much longer distance when you have access to cars and trains.