The objective of this study was to identify the optimal geopolymer binder compositions produced from local industrial by-products and compare them with commercially available materials. The first part investigated the optimal binder composition by studying 27 mixtures. In this part of the research, three series of binders were created: the first series of 18 mixtures was Na-based fly ash-slag, the second series consisted of 8 mixtures of K-based fly ash-slag, and the third series were a mixture of metakaolin-slag based geopolymer. The compressive strengths of the mixtures at the age of seven days ranged from 2.18 to 96.23 MPa. The strength development is clearly defined by the components and proportions of the blends. Geopolymers reach about 80% of their 28-day strength in seven days. The 25% water content was optimal for slag-fly ash geopolymers. The strength of the material increased from 68.08 to 96.23 MPa when the Blaine surface area of the slag increased from 3500 to 4500 cm2/g. The optimal proportions of the alkali solution were the intermediate ratios: SiO2/Na2O = 2.0 and SiO2/K2O = 1.5. In the case where Visonta fly ash is prepared for blending, the fly ash content can be maximized by 30%–50% in addition to the blast-furnace slag. In the second part of the research, mortars were prepared from the selected binders: 4 mixtures were prepared with two different binders. In one of these mortars, the solid part of the binder consisted of local raw materials originating from Hungary. This mixture was prepared with 43 m% fine aggregates. The optimal composition of the tested 27 binders tested was selected as the geopolymer matrix for the production of three further mortar mixtures. In these geopolymer mortars, 55, 65, and 75 m% of aggregate applied. The flowtable values of fresh mortars decreased when the proportion of sand increased. The lower the additive content was, the higher the strength of the geopolymer mortar. The 28-day compressive strengths of filtered fly ash-slag mortar sample with 55%, 65%, and 75% of fine aggregate (F–S-a55, F–S-a65, and F–S-a75) made with the selected optimised filtered fly ash-slag geopolymer binder of group A-I.3 (F–S-A-I.3) varied between 11.39 and 40.15 MPa, whereas the Visont fly ash-slag mortar sample with 43% of fine aggregate (V–S-a43) has been 25.05 MPa. For 28 days, the density ranged between 1870 and 2204 kg/m3. The V–S-a43 is found to be the lowest-density blend. The chloride migration test revealed that geopolymer mortars with higher slag content have higher resistance to Cl− ions.