The COREA (COsmic ray Research and Education Array in Korea) project aims to build a ground array of particle detectors distributed over Korean Peninsular, through collaborations of high school students, educators, and university researchers, in order to study the origin of ultra high energy cosmic rays. COREA array will consist of about 2000 detector stations covering several hundreds of $km^2$ area at its final configuration and detect electrons and muons in extensive air-showers triggered by high energy particles. During the intial phase COREA array will start with a small number of detector stations in Seoul area schools. In this paper, we have studied by Monte Carlo simulations how to select detector sites for optimal detection efficiency for proton triggered air-showers. We considered several model clusters with up to 30 detector stations and calculated the effective number of air-shower events that can be detected per year for each cluster. The greatest detection efficiency is achieved when the mean distance between detector stations of a cluster is comparable to the effective radius of the air-shower of a given proton energy. We find the detection efficiency of a cluster with randomly selected detector sites is comparable to that of clusters with uniform detector spacing. We also considered a hybrid cluster with 60 detector stations that combines a small cluster with ${Delta}{iota}{approx}100m$ and a large cluster with ${Delta}{iota}{approx}1km$. We suggest that it can be an ideal configuration for the initial phase study of the COREA project, since it can measure the cosmic rays with a wide range energy, i.e., $10^{16}eV{leq}E{leq}10^{19}eV$, with a reasonable detection rate.