http://www.real-estate.lviv.ua
Detail info included in English
You can ask the owner directly on the message. (I found the flat here and I didn’t pay any service fee. Even I got discount from the owner.)
http://dobovo.com/
Very detail system like booking.com + Review. Possible to pay on online
Run by one company that it is smaller than above websites. But it has good system that you can check available date. It is only about Lviv
https://www.facebook.com/groups/261332928864/
Secondhand + Renting only in English
https://www.facebook.com/groups/1000696226611238/
In Ukrainian
I do not recommend to use Airbnb to rent a flat.
-The way to lose money is to rent a flat on Airbnb, because you and an owner have to pay lots of service fee PER NIGHT to Airbnb. (Think about how long you will stay. If you stay over 30 days, then service fee *30 times (nights))
-Also Airbnb system is complicating that the owner could charge lots of money on your credit card you wrote on Airbnb after you left. The owner could say like you broke the door, which you didn’t do. Then it is very annoying and complicating to solve. Research about it on google.
-Try to use local website which doesn’t ask to pay lots of service fee or doesn’t interfere about paying that you can pay directly to the owner to avoid service fee.