The problem of optimization of the satellite orbits for local Earth coverage is considered. The class of so-called locally geostationary orbits is suggested and substantiated. It is shown that this class of orbits includes the famous geostationary orbit, the only one circular orbit in the class, as well as an infinite domain of elliptical orbits corresponding to the maximum criterion for the visibility zone of the local Earth region among all possible elliptical orbits. Particular cases of the locally geostationary orbits are Molniya and Supertundra orbit types and some other known orbits. It is shown that optimization in the class of locally geostationary orbits, while the problem of local coverage on elliptic orbits is considered, leads to maximum effectiveness of the resulting choice of orbits and constellations and minimum cost of the optimization process.