If you are a tourist in Ukraine, knowing basics of Russian is useful, the kind that the OP refers to. If you want some business done, just speak English; there would be enough translators. If you need to read something written in Ukrainian, and it is sufficiently complex and your Russian is not very good, have it translated; and even if your Russian is that good, but not your first language, it will cost you a lot of nerves.

(Also, if you know Ukrainian more or less well, it can help significantly to accept Russian, Byelorussian, Polish and Czech. I am not saying you will automatically understand those languages, just that adapting to them should be easier with Ukrainian as the base.)