Nuclear magnetic resonance is detected via the in-plane conductivity of a two-dimensional electron system at unity Landau level filling factor in the regime of the quantum Hall effect in narrow and wide quantum wells. The NMR is spatially selective to nuclei with a coupling to electrons in the current carrying edge states at the perimeter of the 2DES. Interpretation of the electron-nuclear double resonance signals is facilitated by numerical simulations. A new RF swept method for conductivity-detected NMR is introduced which offers more efficient signal averaging. The method is applied to the study of electric quadrupole interactions, weakly allowed overtone transitions, and evaluation of the extent of electron wave function delocalization in the wide quantum well.