We analyse the spatial statistics of the 2D gas-phase oxygen abundance distributions in a sample of 219 local galaxies. We introduce a new adaptive binning technique to enhance the signal-to-noise ratio of weak lines, which we use to produce well-filled metallicity maps for these galaxies. We show that the two-point correlation functions computed from the metallicity distributions after removing radial gradients are in most cases well-described by a simple injection-diffusion model. Fitting the data to this model yields the correlation length lcorr, which describes the characteristic interstellar medium (ISM) mixing length-scale. We find typical correlation lengths lcorr ~ 1 kpc, with a strong correlation between lcorr and stellar mass, star formation rate (SFR), and effective radius, and a weak correlation with Hubble type. Two galaxies in the sample show significantly larger lcorr, and both prove to be interacting or merging systems. We show that the trend of lcorr with SFR can be reproduced by a simple transport + feedback model of ISM turbulence at high SFR, and plausibly also at low SFR if dwarf galaxy winds have large mass-loading factors. We also report the first measurements of the injection width that describes the initial radii over which supernova remnants deposit metals. Inside this radius the metallicity correlation function is not purely the product of a competition between injection and diffusion. We show that this size scale is generally smaller than 60 pc.