That's not what this is about though. NATO is strengthening in those areas because former Soviet countries don't want to go the way of Ukraine and the Crimea. While they may not be a "superpower" in the sense that the United States is, Russia is a very strong world power and can easily rival European countries individually.
The reality is that these Eastern countries asked for NATO membership.
The annexation of Crimea cannot possibly be considered as a starting point.
The EU: tried to establish a free trade zone up to Russia's border, despite having massive trade relations with Russia arguing that Russia's "protectionist economic policy prevents us from having a free trade agreement with them". Consider NAFTA - and Mexico's original exclusion.
Furthermore, when considering the Georgia-Russia war, it's interesting to see the way that Wikipedia portrays the timeline - basically, that Georgia (completely innocently) started suffering from attacks originating in Abkhazia and South Ossetia. Any unbiased European would tell you that Georgia was chomping at the bit to fight with Russia because (drumroll) it thought that it would have USA/NATO backing in an eventual conflict. This is why Abkhazia and South Ossetia were converted into separatist areas (meaning with the territorial conflict in Georgia it will never be able to join NATO) and that's why this was done in Ukraine too.
There was indeed a principled agreement not to expand NATO towards Russia, but all of this started really when the USA excluded Russia from the Marshall Plan (by focusing so much of it on Germany - and look at Germany now, the biggest winner of the Cold War and one of the biggest economies in the world).
It's a difficult thing to explain in a short forum post but Foreign Affairs has some good articles which describe the perspective that Russia has as a failing world power and its need to try to exert force in order to: (i) protect its geopolitical interests and (ii) to be taken seriously.
The Eastern countries you refer to - let's just say as a hypothetical, do you think they would mind - given historical memories - an outright war with Russia? I don't think they'd mind, but that's not what either Russia or the USA want. I can't go into too much detail on some elements in here but what brainchild thought that you could sell a geographically based free trade zone that is extended exactly up to Russia's border, and includes historically important trade partners for Russia, and not include Russia in the negotiation of that process at all?
It's too easy to portray Russia as this big bad villain, but to do so (to me) misses the context of this entire conflict.