Western part of Ukraine doesn't speak Russian. Even if some people there might understand Russian they will not speak it. That's what essentially matters
There are Ukrainians here in Chicago who don't speak Russian but only Ukrainian and English (well, maybe Polish too), the cities you mentioned are all from the Russian-speaking part of Ukraine (except maybe Kiev, which is half Russian)
The Eastern and Southern Ukraine are mostly Russian-speaking. Although Ukrainian is official throughout the country, and many street signs are in Ukrainian, the people use Russian there in their daily conversations. I visited Donetsk region, Kharkiv, Crimea, Odessa and Kiev. All those places are mainly Russian-speaking. Even in the streets of Kiev I was surprised to hear Russian speech more frequently than Ukrainian speech.
As far as I know, the majority of Ukrainian-speaking population are in Western reqions of Ukraine. Lviv is the well-know example.
Well - From the perspective of a foreigner:
I was there and there certainly wasn't anyone who wasn't able to understand my (bad!) Russian. Everyone was 100% up for speaking Russian with me.
Rather, it was me who was totally confused by the signs and writing in Ukrainian.
Admittedly I didn't go to the countryside, I only visited Odessa and Kiev. But I hardly even HEARD anyone speaking Ukrainian, apart from on TV.
However - almost all official signs etc, are in Ukrainian, particularly in Kiev. So for that reason it's not a brilliant place to go to learn Russian. But as for actual interaction between people, it seemed to be Russian, in those places I mentioned. I hadn't given this any thought whatsoever, so I was a bit surprised. I wanted to do "Russian immersion", and Ukraine is not ideal for that, because the Ukrainian language is always present to some extent. My mistake for not informing myself properly.
I think the Black Sea coast of Ukraine is more or less fully Russian speaking.
I spent quite a long time in Belarus and I was very much listening out for anyone speaking Belarussian. I only heard it a couple of times, in a rural place. Some other people in the same village (old ladies) were speaking Polish between them.
I asked lots of people about Belarussian, and older people said they'd love to use it, but they just didn't know it very well. Younger people had done it in school and could use it, but essentially didn't. Some signs are in Belarussian, for example metro stations, and street signs. But almost everything else is in Russian, and all the streets have an alternative Russian name. Some Belarussians have a bit of an accent when speaking Russian, which makes it sound a bit different. They are quite nationalistic about it and WANT to preserve the language. But in reality it's more convenient to speak Russian, so that's what happens. Belarus has only 9 million inhabitants and for books and films Russian has much more to offer - same thing as for all smaller languages.
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