My story takes place in a fantasy/medieval setting, that will incorporate mostly European, most specifically, French medieval inspiration. My main character is traveling from a small village, to a large city within a couple weeks time. In that time, I would like to incorporate an inn or two. The question that I've been trying to figure out, is how close were inn's typically, from one another in medieval Europe/France? I figure that there would be a few close to the city, for those who could not find lodging in town, as it is a very busy place.
Hate to say it varies, but...it varies.
Start with this question, just because it's a wealth of info and tangentially related.:
Which is all about how far apart towns should be. As to inns, you'll want to keep in mind that not all inns were...official inns.
Some of them were homes.
You'd pass by a farmer's house, ask about lodging. Sometimes the farmer would provide it, or could tell you of a farm house where people would take in travellers.
See, when not many people travel through an area, it's not actually profitable to HAVE a dedicated inn. And because Medieval times were far less populated, well...lots of these places won't be.
In larger towns and along trade routes, sure.
As far as cost, some people will be eager enough for news of the road that they will only want chores done in exchange, or entertainment.
The coaching inns that @SudoSedWinifred is citing, were more popular round between 1500-1900, way after Medieval times. There were some during the 1200s, yes, but they are more common later on.
How far apart official inns will be very much depends on how busy the route is. Absolutely they can be further than a day apart.
They'll be in large towns, they'll be in larger cities, and they will be at crossroads on a route,
The inns and innkeepers of medieval England form a poorly documented and neglected group of institutions and individuals. Yet at a time of growing specialism, they were a crucial part of the economic infrastructure of the country. This study is focused on the documentation for central southern England but seeks to place this in a wider perspective. There was now a regular provision of inns in accordance with the size and importance of the towns. Inns generated substantial rent and were evidently felt to be worth considerable investment. Innkeepers were among the rich and influential members of the town. Inns played a vital role in the evolving and prospering economic, social and political life of the nation in this period. SOURCE
The paper I've cited talks about how inns late Medieval inns were connected to the size and importance of a town. Know that the further back in Medieval history you go the less likely there will be official inns. Lots of different places, including monasteries provided succour for the weary traveler, for a fee. There will be plenty of tiny towns, which will only be an outpost, and might not even have an inn. If you ARE NOT travelling along a well-travelled route, like say, the one in the Canterbury Tales (which was along a sort of tourist holy route) actual inns will be rarer.
The tales are presented as part of a story-telling contest by a group of pilgrims as they travel together on a journey from London to Canterbury to visit the shrine of Saint Thomas Becket at Canterbury Cathedral.
A pilgrimage route like that, which would have large groups travelling together--you can bet that that there would be places to stay A LOT more frequently than a day's walk. But whether they would be actual inns--that's going to depend on the surrounding area and population. Many places just have rooms with no beds, just a common room with shelter (bring your own bedroll!) Though from about 1300 there was a boom in private rooms--even then, you might have a bunkmate, really depended on how much $$ you had. Some of the sleeping areas/halls were actually markets in the day time, and when the stalls were packed up, you just slept where you could. paying a small fee for the privilege. And some farmhouses would only take in wealthy travellers.
There were far more travellers AFTER the Black Plague hit, hence more private rooms rather than communal sleeping areas--and far more were opening because people saw travellers looking for a place and finding none, which meant there was a demand. (Though not quite so high as many of them hoped!)
So, in short, the frequency of inns is all about location! As in how many people tend to travel in an area, which is influenced both by time and social factors, like post-plague created a labor shortage that lead to more travel, plus, religion (read:tourism), and trade. On the moors in Scotland for instance--not so many.
On your country road, there might not be any actual inns, but once you get on the trade route there could be lodgings, and the quality and size of those will vary. Don't expect most to be as large as our modern hotels. And expect that some meals will be included in the lodging.
It would be good to analyse old maps of cities and routes, particularly in Europe. Lodgings were typically dispersed along trade routes, as economically and practically these are the ideal locations for them. As in medieval era merchants would normally transport goods from port cities overland to inland cities, they would traverse well-defined and planned routes, stopping for supplies usually on a regular basis.
Along the Silk Route, it is well documented that many 'Trading Posts' were placed several days ride (2-3) apart throughout the route from France, Italy through to Northern India, established almost a thousand years earlier in Roman times when silk was an exotic commodity within the Empire and extant till shipping became the main form of freight.
If your question relates to a location of an Inn in a medieval city, you could look at the typical evolution within a city. Again, origins in European cities are typically derived from ancient Roman cities, where typically they are located at cross roads, with central squares bounded by markets, institutional facilities, religious and military structures, with residential structures surrounding these. All medieval cities have this basic structure thanks to the Romans, Inns would be located usually at intersections surrounding squares and 'arterial streets'. It is not usual to have structures a significant distance from a main square, besides aristocratic villas or farms, for both defensive and economic reasons, until the advent of gunpowder and cannons, where development began to become more dispersed (but only in new forts and newly formed towns, many cities still retained their ancient Roman roots and were of a compact nature).
Going on spec here, putting together snippits from an article in Scientific American on the distribution of sizes in towns and market towns, and a CBC ideas show on alcohol in the middle ages.
Villages generally were no more than 2 hours walk apart, unless there was land that was difficult to use along the way. Reason: An hour is about all the commute people will tolerate. When it gets more than that, it's worth while to make a permanent place to stay.
Small beer (running 1-2% alcohol) was the common beverage. The alcohol killed most harmful bacteria. commenter points out it was likely the act of boiling the water used to brew that made beer safer to drink. A check confirms that 2% alcohol is not an effective bactericide
So unless the town was really tiny it would have a brewery. People could come by with a pail to get a pail of beer to take home. While a much later time, the behaviour is described in the coal towns in wales in "How Green Was my valley." You can also the at the beer ration given to the royal navy.
A brewery makes a good place for people to meet, to socialize, to drink. It's an easy extension for a brewery to offer rooms for the occasional traveler. It also makes a logical place for a traveller to get information. A pub keeper would be up on all the local news and most of the travelling news.
On the other hand, to become an inn would require regular traffic. For a small town, say under 500 people this would likely be more or less mid town. As the towns got larger, an inn is more likely to on the main road at one end or another, as is any business that has more than one or two horses. You want ready access to pasture, and shorter haulage distances for hay and manure.
The physical size of the town is very era and culture dependent. In an orderly culture, where the king's writ is enforced, towns could afford to sprawl. In more chaotic time and place, towns would be walled and as small as possible to make it reasonable to defend the walls. In these places, peasants lived in town. A house by itself was too dangerous. This would mean 1 or 2 room homes, often with a shared wall.
This doesn't give you numbers.
Ok. Let's take a village as having a radius of 3 miles. This gives it an area of roughly 27 square miles. Let's suppose that half is farmable, the rest a mix of woodlot and pasture. 14 square miles of land = 14 * 640 = 9000 acres. It took about an acre to feed someone for a year. A peasant would likely farm 4-6 acres. So our town in principle supports 5 to 7 thousand people. (Assuming around 20% of the food is taxed away) This is large enough to support multiple pubs.
So on that basis in well settled country I would expect to pass several inns a day.
Once you get into rough country, the population density drops. A town in a forest is going to have to import nearly all it's food, and export lumber or charcoal. This sort of economy is not common. A village on the edge of hte forest with a mixed economy is more likely, possibly with camps in the woods where men would work during the week. Still at this remove, I'm betting on an inn or something similar no more than a day apart.
The forest made northern Europe scary. Soils were heavy, and were hard to work with the mediteranean scratch plough. With not much agriculture there wasn't much in the way of civilization. Go reread the Grimm's fairytales.
One of the ways to get an estimate with a bit more meat on it would be to check through parish records of the time. Often they would record the occupation.
Another source would be a translation of the Doomsday Book, the comprehensive survey of England commissioned by the Norman invaders.
Spacing them every "one day's journey" (20 miles for walking, 30 miles for riding) is reasonable.
Busy roads will have more (or larger) inns, and crossroads (around which market towns usually develop) will have even more.