The formerly East Bloc new EU members, if you look up a map, are at the centre of Europe. (Depending on which method and definitions you use, the geometric centre of Europe lies somewhere in Lithuania, in Slovakia or in that mentioned part of Ukraine that was earlier in Czechoslovakia.) You learnt to think of them as East because while the Iron Curtain was in place, it was all just the East Bloc for you. Here however, the region was always called Central Europe (in native languages). Since 1989, on international fora, the compromise term Central-Eastern Europe (CEE) or alternatively Eastern-Central Europe (ECE) has been adopted. (But some even accepted to use Central Europe, for example there is the Central European University, a creation of George Soros with English as teaching language that currently resides in Budapest.)

The geographic ordering also makes some cultural sense: the EU presently extends to the rough border between Catholicism/Protestantism and Eastern Orthodox Christianity. This cultural aspect seems to have counted more in historical relations than shared Slavic language/ancestry (Slovakians, Czechs, Poles are Slavs too but are (were) Catholic), though the latter did count too (say, during WWII).

As for Slovakia, as I mentioned in the diary, there was that Eastern region which was given to the Soviet Union after WWII, and is now Ukraine -- that region was Orthodox majority, but some Orthodox remained in Slovakia too. The Orthodox Carpathian Slavs are often also recognised as a separate ethnicity, the Carpatho-Rusyns.

_{*Lunatic*, n.
One whose delusions are out of fashion.}