The near electric field enhancement around plasmonic nanoparticles (NPs) is very important for applications like surface enhanced spectroscopies, plasmonic dye-sensitized solar cells and plasmon-enhanced OLEDs, where the interactions occur close to the surface of the NPs. In this work we have calculated the near-field enhancement around solid and core-shell alloy NPs as a function of their geometrical parameters and composition. We have found that the field enhancement is lower in the AuxAg1-x alloys with respect to pure Ag NPs, but it is still high enough for most near-field applications. The higher order modes have a stronger influence over the near-field due to a sharper spatial decay of the near electric field with the increase of the order of multipolar modes. For the same reason, in AuxAg1-x@SiO2 core-shell structures, the quadrupolar mode is dominant around the core, whereas the dipolar mode is predominant around the shell. The LSPR modes can have different behaviours in the near- and the far-field, particularly for larger particles with high Ag contents, which indicates that caution must be exercised for designing plasmonic nanostructures for near-field applications, as the variations of the LSPR in the near-field cannot be inferred from those observed in the far-field. These results have important implications for the application of gold-silver alloy NPs in surface enhanced spectroscopies and in the fabrication of plasmon-based optoelectronic devices, like dye-sensitized solar cells and plasmon-enhanced organic light-emitting diodes.