A series of benzoxazine monomers were synthesized based on 3,3′-, 3,4′-, and 4,4′-diaminodiphenylmethane and salicylic aldehyde (P-3,3′-d, P-3,4′-d, and P-4,4′-d, respectively) in order to identify the influence of the position of the amino group in an aromatic amine on the ability of the monomer to polymerize, on its behavior during the polymerization process, and on the structure and properties of the polymers [poly(P-3,3′-d), poly(P-3,4′-d), and poly(P-4,4′-d), respectively] formed during their curing. The chemical structure of all obtained benzoxazines was characterized using 1 H and 13 C NMR spectroscopy. Differential scanning calorimetry was used to study the curing process of benzoxazines as well as to determine the glass transition temperature of polymers based on them. The thermal stability of each polymer was studied by using thermogravimetric analysis. It was found that P-3,3′-d has the lowest melting point and the highest glass transition temperature for poly(P-3,3′-d), and the position of the amino group in the initial diamine does not affect the onset of the polymerization process in the studied benzoxazines. The resulting compounds can be used as components of resins for polymer matrix composites with improved properties.