The NiO4 plaquettes in La2NiO4.17, a cousin of the hole-doped high-temperature superconductor La2-xSrxCuO4, have been studied by Ni-61 NMR in 14 T in a single crystal enriched in Ni-61. Doped and undoped plaquettes are discriminated by the shift of the NMR resonance, leading to a small line splitting, which hardly depends on temperature or susceptibility. The smallness of the effect is additional evidence for the location of the holes as deduced by Schussler-Langenheine et al. [Phys. Rev. Lett. 95, 156402 (2005)]. The increase in linewidth with decreasing temperature shows a local-field redistribution, consistent with the formation of charge-density waves or stripes. For comparison, we studied, in particular, the grandmother of all planar antiferromagnets K2NiF4 in the paramagnetic state using natural abundant Ni-61. The hyperfine fields in both two-dimensional compounds appear to be remarkably small, which is well explained by super (transferred) hyperfine interaction. In K2NiF4, the temperature dependence of the susceptibility and the Knight shift cannot be brought onto a simple scaling curve. This unique feature is ascribed to a different sensitivity for correlations of these two parameters.