To talk briefly about Kiev sightseeing is impossible. Since the moment of its foundation, the city has been growing and developing; new architectural ensembles and historical monuments has appeared during many centuries.
To start getting to know Kiev is better from its main street Khreschatik, which is one of the widest streets in the world. Especially is it very convenient to walk on Khreschatik on the weekends, when the street becomes a pedestrian - this is when you can see in details what Khreschatik is. (by the way the hotel with the same name Khreschatik is located on the main street). Strolling down the street you will be able to evaluate the harmonious combination of different architectural styles and epochs; spend some time in one of the numerous restaurants or cafes; do some shopping. Of course, you can't miss Maidan Nezalejnosti (the Independence Square), which has been reconstructed since the moment Ukraine became an independent country
You can go up the Gorodetskogo street, passing I. Franko theater, straight to the President Palace, which is close to one of the greatest architectural masterpieces of Kiev - the House with Chimeras (architecture is Vladislav Gorodetski)
You just need to go down to the subway and pass one stop from Khreschatik, get off on Golden Gates station and you will find yourself in front of the monument-reconstruction - the ancient Golden Gates which used to be the main entrance to Kiev. Not far from the Golden Gates, there will be Sophia Cathedral, the monument of history of the 11th century. The architecture, frescos and the relics that are kept in Sophia Cathedral will amuse even skeptics. If you have a chance and time definitely come inside. Then, you go through Sophia Square to the monument to Bogdan Khmelnitski, then to Mihailovski Zlatoverhy Cathedral. Turning on Desyatinnaya street, a walker has an opportunity to pass a grand building of Ukrainian Ministry of Foreign Affairs, from there is't no distance to the most bohemian street of Kiev - Andreivsky Spusk.
Those who are tired of walking, can go down from Mihailovky Cathedral to Kontraktovaya Square by a cable car, which is also a sighseeting of Kiev. If you go from Kontraktovaya Square up to Vladimirsky Spusk, you will be able to see a gorgeous view of Kiev, visit Vladimirskaya Gorka(Hill), where the monument to Vladimir the baptizer is, and finish the circle going back through the European square to Khreschatik.
This trip will show you many important and interesting places and monuments, but not all that exists in Kiev and that are worth seeing. Kievo-Pecherskaya Lavra, where except churches and Christian saint places, there are a lot of different museums, Andreevski Spusk with its museums and Andreyevki Church, Askold grave and many other places are worth your attention.