Have fun! My experience of the Ukraine is that, for the most part, it's terrible to ride through. From east to west, I was stopped every few miles it seemed. At first I was throwing dollars out left, right and centre, but then got wise to it and either rode through checkpoints or past police, or just palmed them off with good replicas of my stuff and throttled on out. It's far more corrupt than Russia and makes for slow progress. Also, with the 2012 European championships being held there and Poland, there's so many roadworks that it's just not pleasant.
L'viv is excellent though and Ukrainian folks are good value and their female representatives...do a good job of representing!
Hope this helps ;-)