Astropause radii are estimated for a sample of 70 G stars near the Sun, assuming a solar system model. These estimates are sensitive to total interstellar pressure, including magnetic pressure and the ram pressure of the interstellar medium. G-star space velocities and trajectories are calculated. Three stars within 10 pc of the Sun (HD 2151, HD 20794, HD 190248) have predicted astropause radii larger than 6''. At least eight stars in the sample have traversed low interstellar pressure regions, similar to the path of the Sun, over the last 4 Myr. The Galactic influences on these stellar systems thus may be similar to those on the solar system, providing a list of possibly attractive SETI targets. The closest star to the Sun 4 Myr ago, in this restricted sample, was HD 147513. The stars HD 122742 and HD 126053 are predicted to be part of a previously unidentified triplet system. The relative dimensions of the astropause radii of G stars with space motions parallel and perpendicular to the surrounding interstellar magnetic field may vary by a factor of 2 and may ultimately yield quantitative estimates of interstellar magnetic field strength near the Sun.