As part of the program for the development of local tourism, approved by the Cyprus Tourism Organization (SRT), hotels in Cyprus offer special prices for local residents.
As you know, tourists who purchase "package" tours pay much less for rooms in hotels than if they simply book these numbers directly, because tour operators have an agreement with hotels and redeem numbers by clusters at the beginning of the season. Hotels and tourist apartments that you can book on your own - through online booking systems - in the "hot" season are inaccessible to people with an average income level.
SRT decided to correct the situation and offered additional incentives and benefits to those hotels that will set lower prices for local residents, allowing to rest on the sea or in the mountains to families with medium income.
On link you can find a directory on 2018-2019, compiled by the Cyprus Hoteliers Association (PASYXE) with a full list of hotels (by region of Cyprus) and the cost of living, depending on the season.
However, as the search in popular on-line booking systems has shown, these prices practically do not differ (and sometimes exceed) the cost of accommodation when booking online. In each specific case, it is better to check the cost on the calving site and in booking systems, before making a final decision.