The Monastery of the Caves, a working monastery and UNESCO site above the Dnipro. The Lower Lavra is free, and the caves underneath still hold the mummified monks who dug them.
An 18th century Baroque church at the top of Andriyivskyy Descent, designed by Rastrelli. Free to enter, with an observation deck that's worth the climb on its own.
Blue walls, golden domes and a view over Podil. Free to walk into, and a two minute walk from the top of the funicular.