Here is another deal for those after school holiday deals in August. Based on a family of 4 this is an 8 night holiday from 19/08 and returning on 27/08 in Rhodes. The hotel is the Marietta in Pastida which has good reviews overall compared with the other slightly cheaper places I looked at they had reviews that were far worse! The reviews for the Marietta are below.https://www.tripadvisor.co.uk/Hotel_Review-g674222-d497690-Reviews-Marietta_Hotel_Apartments-Pastida_Rhodes_Dodecanese_South_Aegean.html
You could look at alternative accommodation but I think this represents good value.
The flights are with Norwegian and just include hand luggage. I don't think the flight times are particularly favourable, but it is cheap for school holidays so there are some compromises.
Book flights £468.90 on http://www.norwegian.com
Book hotel £288 on http://www.amoma.com
(I couldn't find any codes that worked)
Book transfers £29.77 http://www.hoppa.com
Total £786.57/£196.64pp based on 2 adults and 2 children