Helium droplets doped with Xe and Kr atoms were photoionized by using VUV synchrotron radiation from the Advanced Light Source and the resulting photoelectron images were measured. A wide range of He droplet sizes, photon energies, and dopant pick-up conditions was investigated. Significant ionization of dopants was observed at 21.6 eV, the absorption maximum of 2p P-1(1) electronic excited state of He droplets, indicating an indirect ionization mechanism via excitation transfer. The photoelectron images and spectra reveal multiple photoionization mechanisms and pathways for the photoelectrons to escape the droplet. Specifically, they show sets of sharp peaks assigned to two mechanisms for Penning ionization of the dopant by He* in which the photoelectrons leave the droplet with no detectable energy loss, a broad, intense feature representing electrons that undergo significant energy loss, and a small amount of ultraslow electrons that may result from electron trapping at the droplet surface. The droplet-size dependence of the broad, intense feature suggests the development of the conduction band edge in the largest droplets seen here (< N > approximate to 250,000).