This is one of the most common questions historians of Russia try to grapple with, and as you might expect the answer is quite complicated. So here goes.
You have to start by defining "Russia". If you're going to speak strictly of Moscow, Novgorod, Kiev (tied very closely to the previous 2 cities historically, obviously not part of Russia now), and St. Petersburg (later), Russia historically had many institutions and political practices which did resemble some found to the west. The land itself was settled by Vikings and most early political history suggests conflict pretty similar to what was happening around the same time in Scandinavia and Northwestern Europe: lots of dynastic struggles, fighting related to conversion to Christianity, etc. While there was a lot about the period that might seem completely alien to us now, the same was true throughout what we now consider Western Europe.
If you're also considering the rest of what's now regarded as Russia, it gets complicated. Russia is itself a modern nation drawn along imperial boundaries. Russia's territory in the Caucasus, Central and Northeast Asia, and Siberia were by no means "Western" in the political or cultural sense historically. Unlike modern Britain, which relinquished virtually all of its empire, Russia has more or less retained its imperial borders, and for many Russians those borders aren't imperial at all, they're entirely natural (Chechen resistance to Russian domination stretches back to the 19th century, but in the eyes of most Russians the Caucasus unquestionably form part of Russia's border).
Where the question gets really interesting is when you consider the ways in which Russian imperial expansion operated: early expansion into Siberia was largely a matter of incorporation of small groups of people, without any particular demands by the Russians for their conversion or resettlement. They were allowed to live where and how they had always lived, and paid tribute like they probably had to other powers before. But Russia's most valuable and important expansion, to the south and into central Asia, came in lands that had been ruled by Mongol forces for centuries. Russia's rule over these places followed Mongolian tradition in many ways - a decidedly non-Western tradition, of course.
When historians assess this sort of thing, they typically look at both policy (like, say, what demands Russia made of newly-conquered peoples) and language (how did Russian rulers claim their right to rule, e.g.). In the Russian empire's most valuable holdings, the evidence points to a very deliberate effort to mimic Mongol rule, which made transition to Russian rule easy for conquered cities' elites, who themselves typically claimed their authority from previous Mongolian rulers. The degree to which this approach was genuine rather than performative is a complicated debate.
To make things more complicated, however, Russian rulers beginning in the late 17th century took a much more Western approach to governance. Peter the Great was famously fond of the West, and while Russia continued expanding in ways which harkened to historical Mongol rule, the pretense was gradually dropped, and Russian rule began looking a lot more like Western imperial expansion: demands for conversion, replacing local elites with imperial officials, etc.
By the 19th century Russian "high culture" was decidedly Western in its orientation. Russian academies brought in scholars from France, Germany, and Britain (causing a major controversy when Russia's founding by Viking traders was pointed out at a foreign scholar's lecture). But for people in the West proper, Russia was not and could never be "truly" Western. Overblown claims about Russian totalitarianism and backwardness certainly had some basis in reality, but they also elided similar circumstances in "true" Western countries, and the discourse quite closely resembled other Orientalist European ideas about the "civilized barbarian" in other parts of the world.
It's worth noting that the designation of "Eastern" and "Western" Europe is a very recent development: from the time of the Roman Empire to the 18th or 19th century, what we now consider "Western" Europe (Britain, France, Germany) was regarded as "Northern" Europe by the intellectual elites of "Southern" Europe (i.e. Italy). The (inherently dismissive) categorization of "Eastern Europe" was as much part of an effort by the intellectuals of "Western Europe" to assert their own preeminence and modernity as it was a reflection of actual difference.