Thanks for the info. Just came back from CY and we managed to park on the street during the night. We just had to move the car back into the hotel's garage for a couple of hours in the morning.

There is a big parking lot on the south side which costs 2 EUR for 3 hours and 10 EUR per day - they close at 7pm and we saw the gate to the lot was wide open after that. The attendant was a grumpy one so we decided to put the car at the hotel garage instead.

I think Motel One charges something similar for parking compared to CY and I think you can get a park and breakfast package with them for EUR 30 per night. We didn't do that because we were on a point stay.