Distances between Medieval towns varied quite widely, as did the population and size.
I think the estimate, and this is a low estimate, for England was that there were over 3,000 deserted Medieval villages that they hadn't discovered.
Now, there are also going to be communities in between smaller than your 400 person population--groupings of families and trading posts along major roads.
Also, not that many people would have lived IN some of these small places. Instead, there were a number of shop keepers, a tavern/inn, maybe a single guard and people who lived and worked inside the village, but for the most part, the population that you might see there would come from those coming in for the day to trade/buy/sell goods, who will later be going back to farmsteads within a day's walk.
A town of, say 3,000 people actually would need about 10 villages and their surrounding farmsteads to support it. SEE LINK
This isn't just a straight line on a road with miles between. A large population place, such as a town or city with like 1,000 people, will actually be surrounded by "satellites" villages adjacent to these larger places. This happened in London--but as London grew, these communities were "eaten up" by the city itself by around the 1700 and 1800s. As to closeness, this rule about "a day's walk away" that people seem to be spouting all over the internet,--that goes right out the window. Many of these satellite villages would only be a mile or two away from their towns--or even less, some would be a scant 1/2 mile. They were not always on a main road, but they would be next to resources (such as water).
Consider as well that some of these towns would be built around a particular thing--a mill for instance--a particular town might be a place where everyone from the surrounding communities come to get their wheat ground, or their leather cured, or something specific to that township. Not every town is going to have the same amenities, and that's important to remember when building them. Not every village is going to have an inn (though it might have people willing to rent a bed).
A town of 3000 would have these 10 or so communities orbiting it--sort of the Medieval version of the suburbs, with a slice of country in between them. So when you were coming up on a real township, you might see more of these small communities, near the larger one--they'd be anywhere from 20 minutes away to 3 hours walk away (12 miles), to a few on the edges that might be as far away as a day's walk. An inn in a town such as this is going to be busy, because travellers just along the road, and traders--people also paid to bed up in barns and sheds nearby--or for a place to park their wagon for the eve.
So your model actually needs to be built with the larger cities placed on the map first.
Then, around each of them, place their satellite villages and settlements. Your max place of 6000--that will need maybe 20 little villages scattered around it. (Some of these won't have more than 50 people in them).
Density and distance between can get weird and really really close in some places, especially when the "orbit" of two cities cross.
In places where there aren't communities/cities of 1000 people to influence the placement of the smaller communities, the density gets lighter. So you might not see any villages for an entire day's walk or ride--this is why some enterprising fellows would set up an inn at a crossroads in the middle of nowhere. They knew people would be travelling, tired, and that there was no chance of anywhere (along the main road anyway) where one could rest, and feel somewhat secure (highwaymen are less likely to visit where there are people).
These less dense places sort of make up for the areas where, every few miles, there's a village...
Even your 400 person village is going to have smaller communities supporting it in this satellite configuration. These will be made up of substantially less people.
As one of the other posters points out, 400 is pretty large.
But let's take a mega-city of the time--London in the 1000s--population estimates are about 10,000-12,000. That means there are going to be about 40 communities surrounding it and supporting it, likely all within a 10 minute walk to about 3 days walk, because it's so large.
By 1337, the London population had grown considerably. Here's an estimate of the population of largest cities from wikipedia, which I am adding because you've said your numbers are arbitrary, and it's good to have a basis:
- London 23,314
- York 7,248
- Bristol 6,345
- Coventry 4,817
- Norwich 3,952
- Lincoln 3,569
- Salisbury 3,226
- King's Lynn 3,217
- Colchester 2,955
- Boston 2,871
- Beverley 2,663
- Newcastle 2,647
- Canterbury 2,574
- Bury St Edmunds 2,445
- Oxford 2,357
- Gloucester 2,239
- Leicester 2,101
- Shrewsbury 2,083
- Great Yarmouth 1,941
- Hereford 1,903
- Cambridge 1,902
- Ely 1,772
- Plymouth 1,700
- Exeter 1,560
- Hull 1,557
- Worcester 1,557
- Ipswich 1,507
- Northampton 1,477
- Nottingham 1447
- Winchester 1,440
Keep in mind that there are lots of smaller communities surrounding each of these. A city of 6,000 would not be at all common by the standards of Medieval times. Just throwing out these numbers and specific cities to give you a base. Add to this that the low estimate of the number of Medieval villages that we HAVEN'T discovered yet is 3,000--and you'll see that the landscape was likely teeming with tiny villages along the way, with some less populated areas in between.
As other posters have pointed out, the more farmable the land, the closer settlements are to one another. In the densest places it's going to be about one every mile or two (and there will be some very close to large cities). These communities are going to be tiny, but EVERYWHERE, with farmland in between.
Please see the fantastic video in Giant Cow's answer--this distance is a pretty good yardstick for world-building (about 10 miles between each sizable town, which means that there's a town is within 5 miles for everyone) for places that are not as richly farmable, and less influenced by the larger cities. Medieval towns were different because of the factors I have outlined, often closer, much smaller, and with more distance in between settlements where farming was impossible or there was woodland.