We analyze the local structure of two-dimensional packings of frictional disks numerically. We focus on the fractions x(i) of particles that are in contact with i neighbors, and systematically vary the confining pressure p and friction coefficient mu. We find that for all mu, the fractions xi exhibit power-law scaling with p, which allows us to obtain an accurate estimate for x(i) at zero pressure. We uncover how these zero pressure fractions x(i) vary with mu, and introduce a simple model that captures most of this variation. We also probe the correlations between the contact numbers of neighboring particles.