A survey of interstellar Na I D1 and D2 absorption features in the spectra of 104 early-type stars in the second and third Galactic quadrants reveals the large-scale kinematics of the interstellar gas within the Galactic anticenter hemisphere at distances from the Sun between ~70 and ~250 pc. Employing a technique that uses both the radial velocities and column densities of the Na I absorptions produced by the intervening gas we have identified the velocity vectors and determined the spatial distribution of eight interstellar clouds in the volume explored. The average internal H I+H2 densities of the clouds range between 0.03 and 1.7 cm-3, and their masses between 80 and 104 Msolar, although uncertainties in the sizes of the clouds, their possible extension beyond the region explored, and the presence of denser gas embedded in the larger clouds imply that these will tend to be lower limits. We have clearly identified clumps of denser gas immersed in the low-density gas in one of the clouds; these clumps show internal H I+H2 densities of order 50 cm-3. Although we are not able to detect any interstellar Na I within 70 pc, the sizes of some of the clouds imply that their near edges are within that range of distances from the Sun. With respect to the local standard of rest the clouds move with velocities between 19 and 54 km s-1. Their velocity vectors do not support the view of a local interstellar medium uniquely dominated by expansion from centers in the Scorpio-Centaurus OB association; our results suggest that this expansion is present in the Galactic center hemisphere but in the Galactic anticenter hemisphere is restricted to the immediate neighborhood of the Sun.