We study nucleation of liquid droplets from a one-component vapor phase on a planar lyophobic substrate, delta, patterned with a number of lyophilic (easily wettable) circular domains, gamma. The wettabilities of the lyophilic domains and the lyophobic substrate are characterized by contact angles theta(gamma) and theta(delta), respectively. Depending on the supersaturation of the vapor and on the contact angles theta(gamma) and theta(delta) nucleation of a droplet on one of these circular domains proceeds through a free energy barrier with one or two maxima (a double barrier). Barriers with two maxima occur for intermediate values of the supersaturation. In terms of the dimensionless supersaturation Delta, this intermediate regime is given by sin theta(gamma) < Delta < sin theta(delta) for (theta)gamma < theta(delta) < pi/2 and by sin thetagamma < Delta < 1 for theta(gamma) < pi/2 < theta(delta). We extend classical nucleation theory to account for the kinetics of nucleation through a double barrier and apply this extension to the nucleation of droplets on lyophilic circular domains.