Okay, I'm following up on my promise to discuss floo powder in my answer. I'll talk about a few other things, but this is a great opportunity for me to geek out and actually accomplish something while doing it.
Section 1: The Floo network (TL;DR - some forms of transportation will be rendered obsolete only when the system becomes available to all people)
For those who don't know, floo powder is a fictional substance used a few times in the Harry Potter books and films. It's a cheaply purchased powder (2 Sickles a scoop) that is readily available to pretty much all witches and wizards. Your teleportation system probably doesn't involve this powder, but I can still discuss the social aspects of such a system.
Floo powder allows one to travel through the Floo network, which in the Harry Potter franchise is a network of fireplaces. One thing that is different about this is that any fireplace can be for this, but according to Arthur Weasley, the fireplace must be connected to the Floo network in advance. So I suppose it is really an analog to an easy-to-set-up teleportation station.
The Floo network is used pretty much how I think your teleportation system would work - for some minor travels (i.e. to shop), as well as commuting to and from work. It is important to note that this does not render normal transportation obsolete, because of the many other ways to get from one place to another (I'll ignore Apparition because it has no place in your world). I would assume static teleportation would have the same effects in your world, and would have the same uses. One major thing to note is that because vehicles and other objects can be taken with the person, many forms of transportation for goods would be rendered obsolete. You wouldn't need a horse and wagon to get from one place in town to another if there were teleport stations set up near where you wanted to leave from and go to.
So we've established that many forms of transportation would be rendered obsolete. But this is only if the stations were widely available. In your scenario, they are a privilege that only a few can use regularly. For this reason, many forms of transportation would not be rendered obsolete - yet. I would guess that, over a period of time (many decades, granted), the system would become readily available to the general public, and the system would resemble more the Floo network. I could make other comparisons here, most notably the New York City subway system or the London Underground, but I doubt these are necessary, and would only apply when the system becomes ubiquitous.
Section 2: Warfare (TL;DR - the system could be a big problem if enemy forces get control of it)
This is actually the first thing that popped into my head, partly because I recently took a look at another question involving technology and warfare. The following scenario would only be an issue if the system proliferates - but then it would be a huge problem.
One of the great things (or bad things, depending on your perspective) of a Renaissance-like society is that wars are so darn slow. Well, troop movements, at least. Assuming you've read at least one book when you were young that revolved around a Middle-Ages-esque epic good-vs-evil premise (and if you haven't, go out and read one right now!), you know that it takes an army (or even a few individuals) a long time to get from Point A to Point B. That's really good for a second army if the first army is attacking their fortress/castle/town/other-settlement because if they have any scouts at all, they will know in advance (even if it's only an hour or two) that the enemy is coming, and they have time to rouse the soldiers and get the other citizens to safety.
That all comes crashing down with the advent of this teleportation system. True, there are only a few teleport stations (again, unless the system develops), but even a single terrorist could potentially climb on one and set off a bomb (medieval-style) in the city center. Scary stuff. If the teleport cubicles are available to all, that means that multiple terrorists could get through - or even a small army. Defense forces would have absolutely no warning, and a city could be taken within a very short period of time.
By the way, long after writing this answer I found this question, which discusses this point in more detail.
Section 3: Relations between nations (TL;DR - everyone gets to know everyone else)
This is the last bit. I promise.
Anyway, lets look at the history of our world - or rather, some bits from the Age of Discovery onwards.
In fourteen hundred ninety-two
Columbus sailed the ocean blue.
He had three ships and sailed from Spain
He sailed through sunshine, wind and rain.
Christopher Columbus first reached "The New World" in 1492. He was an Italian but sailed for Spain, funded by Queen Isabella and King Ferdinand. After such a momentous voyage, one would think that Spain (and everyone else in Europe) would be eager to colonize (or at least make friends with the folks who were already living in "The New World" - naaaah), right?
Well, everyone else in Europe was pumped up about the new opportunities that lay ahead. The trouble is, it took time. Things really didn't start rolling until the early 1500s, and even after that, colonization wasn't exactly smooth sailing (pun absolutely intended). The first players were Portugal and Spain, thanks in part to the Treaty of Tordesillas. It took decades for other European nations to get hand- and foot- holds in "The New World".
Would this static teleport system have made things any easier? Probably not at first. It is true that Span and other countries would have invested a lot to get a few stations over in the Americas because of how long it took to cross the Atlantic, but there wouldn't have been a whole lot while the technology was in its early stages. But I can almost guarantee you that, whatever phase the teleportation system was in prior to a Columbus-esque discovery, it would be very much improved afterwards. So it would definitely make relations between nations easier, because travel would be much quicker.
What you should get out of this is that such a system might not have a revolutionary impact at first if the system was only readily accessible to a few people. There would be other problems to solve, such as just where the power for this whole thing comes from. But I think that the technology would be developed pretty darn quickly once people saw its uses. It could lead to faster transport of people and goods, quicker and deadlier warfare, and better international relations.