I'm from Lvov and you can tell my nationality from the way I spell the name. The reason I bring up this distinction is because there is a lot of bad blood between Ukrainians and Russians, specifically in my home town (en.wikipedia.org/wiki/Lviv#World_War_II_and_Soviet_occupation). Not that it matters, but the two languages/nationalities are not interchangeable there, like they are anywhere else. This means you can inadvertently insult a young person, especially if they had their grandparents go through some shit on either side.
If you want to impress someone, guess their nationally by the way their last name ends. Russian male last names typically end on consonant, e.g., Medvedev, Putin, Sidorov. Append an "a" (pronounced "Ah") to make a female last name, e.g., Medvedeva, Putina, Sidorova. Ukrainian last names typically end on a vowel, e.g., Kuchma, Yushenko, Timoshenko, and do not have a male/female versions.
Other than that, the city is beautiful and I visit the tourist traps every chance I get. For example, did you know Lvov is THREE times as old as America? The ENTIRE downtown, not just some building or a street, are on the Unesco "this is good shit" list. They also have the only one SITTING STATUE OF LIBERTY (ask a local, or better yet one of them grandpas playing chess downtown, also I hear students majoring in history give the best tours
The opera and ballet theater is seriously hot fire. I think it is ranked third in the world or something. If you've never seen a ballet, this is the place to do it. At first I thought it was gay, but the women on stage are incredible. Think of it as a classy excuse to stare at gorgeous, thin, fit women from a distance. Extra points if you use binoculars
The view from High Castle (Vysokiy Zamok) and some of the downtown top floor cafes are pretty awesome. Oh and the beer, the beer is my favorite. It tastes nothing like the donkey piss they sell in the states. For some reason they always serve it with a glass. I guess it is meant to make one feel classy or do something to the beer aroma.
Try this one time, go to that one movie theater downtown, order a beer at a cafe next to it, and count the number of 8s or better walking by. Last time I did it, I ran out of fingers before I could finish a beer
My first impression when I came back was that everything is tiny and dirty and everyone smokes and stinks, but I guess you could say that about all Europe. Anyway, the women are gorgeous and they will fuck you in a heartbeat for a chance to pursue the American dream. Being an American typically entails that you are a good person, you do not hit women, avoid drinking binges, and have a paycheck that is not delayed for 3 month at a time. Things might have improved recently, but thats the way I remember it growing up. Just for reference, a good salary is $400-500/month, a cab to anywhere in the city is about $10, and a beer costs like $2-3. By the way ALL PRICES ARE NEGOTIABLE, but you've got to know how to do it. Unfortunately, I never developed that skill.
Having your own place to stay is huge as most young people stay with their parents well into their 20s or until they get married. My point is that if you ask a girl out and invite her over to your place, that's a huge plus. Don't bother asking if she's got a man or not, she's not fucking you out of romance, she's playing an angle. Like Mystery said, most of the "game" in Eastern Europe is simply throwing money around. The fucked up thing is that the local dudes would not be doing it, if it did not get them laid. Having an accent, a credit card in your wallet, and some decent clothes that distinguish you from the tourist crowd has the same effect, but it is more subtle and keeps the pussy wet all day. Getting out of Ukraine is such a huge dream for them that all you have to do is hint at the fact that you're looking for a wife and she'll fuck you just to secure her place in the lineup. Do you think I'm making this shit up? Have someone translate this story for you (NSFW text): anekdot.ru/id/520275/ I suggest you find a native because I don't trust that Google Translate will capture all the delicious irony.
P.S. There are NO non-white people there. I lived through half my teens and I've only seen one black dude and possibly an asian lady EVER. I think she was a mix though.