Hi,
No issues - make sure you have your green card and original documents. Usually quite long ques at the border - but people are usually happy for you to make your way close to the front with the bikes. Found the Slovak border crew to be very uptight - the Ukrainians more freindly - learn a few basic phrases in Ukraine and you will get a big smile.
Leaving the Ukraine - make sure to take some good vodka with you ... it is complulsary - I was told be a customs guard that I had a big problem... until I showed him my hidden stash!!
uzhgorod and the Transcarpatia region of the Ukraine ( SW) is really nice - and you can loop back through Romania as well - if yu need any advice pm me
gavin