You could find shoe repair shops in every district of Kyiv. Usually your shoes will be repaired within a day or so. The most common and wide spread shoe fix in this part of the world is to change or add heel-taps (to heel a pair of shoes). In Ukrainian it will sound like: "postavyty nabeeiky na toofli". In Russian it will sound like "postavit' naboiki na toofli".

Another shoe fix is to put or change "Prophylaxis" on the bottom of the shoe sole. In Ukrainian it will sound like: "postavyty profeelaktykoo". In Russian it will sound like "postavit' profeelaktikoo".

Dictionary:

Shoe repair shop - in Ukrainian "Remont Vzoottya", in Russian "Remont Oboovi" ;
Shoes- in Ukrainian "Toofli", in Russian "Toofli";
Boots - in Ukrainian "Cherevyky", in Russian "Botinki";
Sole - in Ukrainian "Pidoshva", in Russian "Podoshva";
Heels - in Ukrainian "Kablooky", in Russian "Kablooki".