Regarding apts in Kyiv, there doesn't seem to be much variation from month to month. Or perhaps my prices have been similar because I usaully come during late spring and early fall.
Anyway, I usually pay around $35 per night for one bedroom, living room, kitchen and bath. Sometimes I get two bedroom for around $40. I never live right in center, but go no further out than about two metro stops. I also insist on being within a 10 min walk of metro, or stop another transport form such as minibus, trolley or tram.
Also on my insist list is ten minutes to western style supermarket, internet cafe, decent moderate priced restaurant, etc.
Great bargains here on ballet, concerts, etc.
Can go to world class ballet for 4-6 dollars and concert for less than 2 dollars. Have been to 2 ballet and 3 concerts so far.
Great cheap food also, or can spend near western prices if want to go to those in major hotels. The gals like to go there once in a while, but I drop any who push for going there frequently.