  In Er$^{3+}$:Y$_2$SiO$_5$, we demonstrate the selective optical addressing of
the $^{89}$Y$^{3+}$ nuclear spins through their superhyperfine coupling with
the Er$^{3+}$ electronic spins possessing large Land\'e $g$-factors. We
experimentally probe the electron-nuclear spin mixing with photon echo
techniques and validate our model. The site-selective optical addressing of the
Y$^{3+}$ nuclear spins is designed by adjusting the magnetic field strength and
orientation. This constitutes an important step towards the realization of
long-lived solid-state qubits optically addressed by telecom photons.
