X-rays are generated throughout the heliosphere and the terrestrial magnetosheath as a consequence of charge transfer collisions between heavy solar wind ions and interstellar and geocoronal neutrals, respectively. Simple models of this X-ray emission have been presented in the past, but results from a more sophisticated model are described in this paper. In particular, to obtain the densities of interstellar neutrals our X-ray model uses to determine X-ray intensities, we use the Fahr <1971> hot model although with recently determined input parameters. The geocoronal X-ray model we use in this paper has also been improved, as described in a recent paper by Robertson and Cravens <2003>. In previous papers we demonstrated that there is significant correlation between the long-term enhancement part of the soft X-ray background measured by the R¿ntgen Satellite (ROSAT) and the solar wind proton flux. In the current paper we determine the steady-state X-ray intensities due to the interaction between the solar wind and both interstellar neutrals and the geocoronal neutrals as a function of look direction and time of year. X-ray intensity maps are shown for both a spherically symmetric solar wind and for a latitude-dependent solar wind (i.e., fast and slow solar wind regions). In all cases, the X-ray intensity is highest when the view direction is towards the Sun, but the intensity is also relatively high for view directions intersecting the gravitational focusing cone of interstellar helium. We also show a heliospheric/geocoronal X-ray intensity map for the conditions used by Snowden et al. <1995> in producing the 1/4 keV channel soft X-ray background map in galactic coordinates. Our preliminary conclusion is that very roughly 50% of the total background soft X-ray intensity in the galactic plane and 25% at high galactic latitudes can be attributed to the charge transfer process operating within the solar system, with the remaining emission coming from outside our heliosphere.