Cyprus, of course, is a resort place and pricing here depends on the season. Especially in the case of short-term rentals. Also, a city/district influences the cost - there are more expensive places and low-budget ones.
The most interesting, modern, and beautiful city in Cyprus is Limassol. Here, one can find the most comfortable, contemporary, and expensive property to rent. For example, one-bedroom apartments in a good house in Limassol can cost out of season from 120€ per night. The prices for spacious luxury apartments and villas are 6000-15000 € per month, and daily rent will cost more. A room in a modest three-star hotel costs 55-60 € per day. At the same time, one can rent an apartment with two bedrooms in a good area of Limassol for a year for 1000€ per month. With two deposits and a commission to the agent, but nonetheless.
The most budget city in Cyprus is Larnaca and its surroundings, especially Dhekelia. Renting a studio for a short term out of season will cost 400 - 500 € per month. Long-term rental will be 300 - 500€ depending on the quality of the accommodation and the area.
Protaras is a beautiful place, but exclusively for relaxing by the sea. Rental prices are close to those in Limassol, but one will not find any urban infrastructure here.
In Paphos, rentals are very different, and one can find both budget and luxury accommodation here. The minimum long-term rental in Paphos is 500 € per month, short-term - from 40-50 € per day.
Nicosia has good quality budget accommodation. Long-term rent of even a house will cost 350-400 € per month.