Four new manganese germanates and silicates, A2MnGeO4 (A = Li, Na) and A2MnSiO4 (A = Na, Ag), were prepared, and their crystal structures were determined using the X-ray Rietveld method. All of them contain all components in tetrahedral coordination. Li2MnGeO4 is orthorhombic (Pmn21) layered, isostructural with Li2CdGeO4, and the three other compounds are monoclinic (Pn) cristobalite-related frameworks. As in other stuffed cristobalites of various symmetry (Pn A2MXO4, Pna21 and Pbca AMO2), average bond angles on bridging oxygens (here, Mn-O-X) increase with increasing A/X and/or A/M radius ratios, indicating the trend to the ideal cubic (Fd3̅m) structure typified by CsAlO2. The sublattices of the magnetic Mn2+ ions in both structure types under study (Pmn21 and Pn) are essentially the same; namely, they are pseudocubic eutaxy with 12 nearest neighbors. The magnetic properties of the four new phases plus Li2MnSiO4 were characterized by carrying out magnetic susceptibility, specific heat, magnetization, and electron spin resonance measurements and also by performing energy-mapping analysis to evaluate their spin exchange constants. Ag2MnSiO4 remains paramagnetic down to 2 K, but A2MnXO4 (A = Li, Na; X = Si, Ge) undergo a three-dimensional antiferromagnetic ordering. All five phases exhibit short-range AFM ordering correlations, hence showing them to be low-dimensional magnets and a magnetic field induced spin-reorientation transition at T < TN for all AFM phases. We constructed the magnetic phase diagrams for A2MnXO4 (A = Li, Na; X = Si, Ge) on the basis of the thermodynamic data in magnetic fields up to 9 T. The magnetic properties of all five phases experimentally determined are well explained by their spin exchange constants evaluated by performing energy-mapping analysis.