I really can't tell how safe is Ukraine for a foreigner, because I'm a resident and some things that can be problematic for a person who is not fluent in Russian/Ukrainian obviously go unnoticed by me, or do not apply to me.
But I agree with CoffeeCup. Moldova and even Romania seem more dangerous from where I stand. I'm not sure about Transdnestr Republic, I think it's about as safe as Belarus, which is pretty safe (but I've never been there).

I visited Kiev (Kyiv) last summer. People were friendly and mellow. I was surprised by the number of people who spoke Ukrainian (about 15-20%, I expected less than that), but everyone understands Russian of course, so it should not hinder a Russian speaking traveler in any way. I stayed in a hostel, and there were a lot of foreigners from all over the world. All of them looked happy enough, I did not hear about any serious problems. Since it was center of the city, there were plenty of polcemen even after midnight (I've never seen so many of them in my city ).
I can post some photos, if it can help you to make a decision. Unless (judging by your last post) you've already decided to visit Odessa?