We model the modification in the spontaneous emission (SE) rate of an emitting dipole placed on the surface of a two-dimensional (2D) L3 optical nanocavity using 3D FDTD calculations. We show that by introducing a concave region into the cavity-surface, the cavity Q-factor is largely unaffected, however the electromagnetic field intensity at the dielectric-air interface is significantly enhanced compared to a regular L3 (planar) structure. Our calculations indicate that such a modification of the cavity surface leads to peak emission intensity enhancements (at the cavity-mode resonance) for a dipole emitter of 0.1 nm linewidth by a factor of 33 times. For an emitter having a linewidth of 12 nm, a peak intensity enhancement of 43 times is predicted. Finally, we show that enhancements of up to 42 times in SE rate can be expected for surface-bound (organic) emitters, with our structures having possible applications as nanosensor devices and single-photon light-sources.