We report on the syntheses, crystal structures, and magnetic susceptibilities of a family of copper pyrazine (pz)-based antiferromagnets with moderate in-plane magnetic exchange. These materials fall into two classes: monoclinic complexes [Cu(pz)2]A2 for A = ClO4 (1) or BF4 (2) and the tetragonal complex [Cu(pz)2(NO3)]PF6 (3). Compound 1 and its deuterated version [Cu(pz-d4)2](ClO4)2 (1a) crystallize in the space group C2/m at room temperature with disordered perchlorate anions. For both 1 and 2, the C centering of the Cu(II), S = 1/2, site yields four equivalent nearest neighbors, producing layers of Cu(II) ions bridged by the pz molecules, which map onto a square magnetic lattice. The layers are offset such that Cu(II) ions lie above and below the holes of adjacent layers. Compound 3 crystallizes in the space group I4/mcm with a layer structure similar to those of 1 and 2 but with Cu(II) ions of adjacent layers stacked above each other and bridged by semicoordinate NO3- ions. The variable-temperature susceptibilities in these compounds approximate a two-dimensional Heisenberg antiferromagnet with J values within the layers of 17.5(3) K (1), 15.3(3) K (2), and 10.8(3) K (3). Ordering transitions are observed in the magnetic data at 4.2(3) and 4.3(5) K for 1 and 2, respectively.