We address topological currents in polariton condensates excited by uniform resonant pumps in finite honeycomb arrays of microcavity pillars with a hole in the center. Such currents arise under combined action of the spin-orbit coupling and Zeeman splitting, which breaks the time-reversal symmetry and opens a topological gap in the spectrum of the structure. The most representative feature of this structure is the presence of two interfaces, inner and outer ones, where the directions of topological currents are opposite. Due to the finite size of the structure, polariton-polariton interactions lead to coupling of the edge states at the inner and outer interfaces, which depends on the size of the hollow region. Moreover, switching between currents can be realized by tuning the pump frequency. We illustrate that currents in this finite structure can be stable and study bistability effects arising due to the resonant character of the pump.