We apply recently developed effective field theory nuclear models in mean field approximation (parameter sets G1 and G2) to describe ground-state properties of nuclei from the valley of $\beta$-stability up to the drip lines. For faster calculations of open-shell nuclei we employ a modified BCS approach which takes into account quasi-bound levels owing to their centrifugal barrier, with a constant pairing strength. We test this simple prescription by comparing with available Hartree-plus-Bogoliubov results. Using the new effective parameter sets we then compute separation energies, density distributions and spin--orbit potentials in isotopic (isotonic) chains of nuclei with magic neutron (proton) numbers. The new forces describe the experimental systematics similarly to conventional non-linear $\sigma-\omega$ relativistic force parameters like NL3.