One outstanding question to be addressed in assessing the risk of exposure to space travelers from galactic cosmic rays (GCR) outside the geomagnetosphere is to ascertain the effects of single heavy-ion hits on cells in critical regions of the central nervous system (CNS). As a first step toward this end, it is important to determine how many ``hits'' might be received by a neural cell in several critical CNS areas during an extended mission outside the confines of the earth's magnetic field. Critical sites in the CNS: the macula, and an interior brain point (typical of the genu, thalamus, hippocampus and nucleus basalis of Meynert) were chosen for the calculation of hit frequencies from galactic cosmic rays for a mission to Mars during solar minimum (i.e., at maximum cosmic-ray intensity). The shielding at a given position inside the body was obtained using the Computerized Anatomical Man (CAM) model, and a radiation transport code which includes nuclear fragmentation was used to calculate yearly fluences at the point of interest. Since the final Mars spacecraft shielding configuration has not yet been determined, we considered the minimum amount of aluminum required for pressure vessel-wall requirements in the living quarters of a spacecraft, and a typical duty area as a pressure vessel plus necessary equipment. The conclusions are: (1) variation of the position of the ``target site'' within the head plays only a small role in varying hit frequencies; (2) the average number of hits depends linearly on the cross section of the critical portion of the cell assumed in the calculation; (3) for a three-year mission to Mars at solar minimum (i.e., assuming the 1977 spectrum of galactic cosmic rays), 2% or 13% of the ``critical sites'' of cells in the CNS would be directly hit at least once by iron ions, depending on whether 60 mum^2 or 471 mum^2 is assumed as the critical cross sectional area; and (4) roughly 6 million out of some 43 million hippocampal cells and 55 thousand out of 1.8 million thalamus cell nuclei would be directly hit by iron ions at least once on such a mission for space travelers inside a simple pressure vessel. Also, roughly 20 million out of 43 million hippocampal cells and 230 thousand out of 1.8 million thalamus cell nuclei would be directly hit by one or more particles with z >= 15 on such a mission.