I used this service when in Kiev in September.
http://kievluxapartment.com/Good apartment right near Arena and a few minutes walk from Kreshatik (but they have many)...
Good service, great rates on airport transfers and very reliable... no shonky rip offs you'll get from the guides...
Airport transfers were $30 I think... after dropping us in the centre the driver INSISTED on taking me to buy groceries because we had arrived late at night with two infants and then when we got back to the apartment he refused to take extra money for the extra 45 minutes or so.
I would recommend them, but caution you to confirm EVERYTHING before arriving - because I trust no one when traveling.