Everyone who traveled to Ukraine can confirm that Ukraine is an amazing place to visit. For centuries, it's been influenced by both East and West, which has shaped its culture. However, most part of Ukraine has always been a part of the European Civilization. Western Ukraine (Galicia) has been a province of the Austrian-Hungarian Empire, and later, between the two world wars, a part of Poland. Since reclaiming independence from Russia in 1991, Ukraine proclaimed its strategic goal to join the European Union, and has been building a pure market economy and diverse civil society. It's not an easy task, but it's fair to say that Ukraine is one of the most democratic countries of the former USSR, excluding three Baltic countries which are now in the EU.
Modern Ukraine is a good place to travel by bicycle, even though almost none segregated cycle infrastructure has been built yet. Almost all roads in Ukraine, except for those connecting major cities, have two lanes, light traffic, and their surfaces are usually in a relatively descent condition. Most roads in Ukraine are suitable for travelling by bike, except for major international highways. The most popular destinations among Ukrainian and foreign cycling tourists are the Crimean peninsula on the Black Sea and the western part of the country, including the Carpathian mountains with their unique culture.
Ukraine has a relatively well-developed tourism infrastructure, with hundreds of small hotels, motels and diners established over the last decade. They normally offer a nice combination of good quality and low prices.
Unlike some other post-Soviet countries, Ukraine is an open country offering a visa-free entrance for EU and US citizens and requiring no mandatory police registration for tourists. In terms of safety, Ukraine has a very low crime rates, and some basic road safety precautions like wearing bright clothes, helmets and using flashlights will help ypu avoid road accidents.
To find out more about traveling Ukraine by bike, please watch this 13-minute film made by a copule of Dutch travelers who discovered Ukraine in summer 2012: