Smolensk would be located just on the very border (or even across the border) of this state. Based on the map, major Medieval cities in this area would be Polotsk (big, but relatively close to the border as well), Vitebsk, Drutsk (in the very center of that territory), and Minsk.
On another note, I have a general question. What's the level of technological development in this timeline? I'd imagine it's non-linear and is different for different areas of knowledge and in different regions.
To make it easier, how would you rate technology for the following areas?
- math and abstract sciences
- applied sciences (physics, chemistry)
- biology and medicine
- mechanical engineering and metallurgy
- communications, architecture and infrastructure
- naval and land military science
- politics, bureaucracy, and administration
- economics
- social sciences
Thanks, I'll go with Minsk.
It's actually good that you asked this, since it is very important. I'll go through them:
-As far as mathematics goes, generally, we're a few decades ahead of OTL. Calculus developed in 16th century South India and spread from there to elsewhere. Physics and chemistry are also a few decades ahead of OTL (I'd peg it around an equivalent of 1750), and are progressing quickly in the Persian milieu. To wit, astronomers are well aware of the nature of the Milky Way, and thermodynamics has just started to become a field of study.
-Medicine is still somewhat behind OTL, and is still in a somewhat medieval frame of mind as to how it's practiced in regards to hospitals and such - this is mostly what is holding it back, though certainly the ongoing scientific revolution is changing this as well, at least in the Middle East.
-Metallurgy (and engineering in general) is also slightly ahead of OTL, helped along by the improved knowledge of physics and chemistry. In another little side note, the knowledge of how to make Damascus steel was never lost.
-Western Europe is the most advanced in naval technology, just from having done the most long-distance sailing of anyone. The sextant is in fairly common use by now. North Africa isn't far behind. Militarily, there's not really any particular region that is ahead in military science/tactics/whatnot.
-Political science and thought is about the same as OTL - except on matters of religion. The Middle East is entering a phase where religion and government are starting to separate. After undergoing a sequence of religious wars Persia (thanks to a continuing Zoroastrian minority) has de facto accepted a policy that's similar to laïcité, and to a lesser extent Egypt (a formerly Catholic dynasty ruling over a majority Muslim population) has followed. Ideals about human rights and the social contract and whatnot that were in the OTL Enlightenment are cropping up in the same region but aren't nearly as influential as they were in OTL, at least not yet.
-Economics and social sciences are both about the same place they are OTL about this time; i.e. pretty much in their infancy.
As far as all this goes, the largest intellectual centre of both science and philosophy right now is undoubtedly Persia, specifically, the cities of Isfahan and Nishapur. In fact, Persian is the primary scientific language of most of the region (and even as far away as Greece and South India) and most scientific texts are written in Persian (and a lot even follow in the tradition of writing in rather melodramatic poetic verse). India, North Africa, and parts of the Mediterranean shore of Europe (like Italy and Greece) largely follow in this sphere.
In East Asia, which I also probably should mention, the mess that China has been in for the better part of the last century has left it somewhat behind. The Japanese sphere is the most advanced in most aspects here, certainly helped along by Japan's greater contact with the outside world. However, with this period in China appearing to be at an end this appears to be ending. Southeast Asia mostly acts as an auxiliary to the Indian subcontinent.
edit: Also keep in mind that a lot of scientific advancements are coming from a the Middle Eastern tradition, not the European one. That changes a fair bit.