We demonstrate a novel scheme for plasmonic nanofocusing with internally illuminated asymmetric metallic pyramidal tips using linearly polarized light. A wafer-scale array of sharp metallic pyramids is fabricated via template stripping with films of different thicknesses on opposing pyramid facets. This structural asymmetry is achieved through a one-step angled metal deposition that does not require any additional lithography processing and when internally illuminated enables the generation of plasmons using a Kretschmann-like coupling method on only one side of the pyramids. Plasmons traveling toward the tip on one side will converge at the apex, forming a nanoscale "hotspot." The asymmetry is necessary for these focusing effects since symmetric pyramids display destructive plasmon interference at the tip. Computer simulations confirm that internal illumination with linearly polarized light at normal incidence on these asymmetric pyramids will focus optical energy into nanoscale volumes. Far-field optical experiments demonstrate large field enhancements as well as angle-dependent spectral tuning of the reradiated light. Because of the low background light levels, wafer-scale fabrication, and a straightforward excitation scheme, these asymmetric pyramidal tips will find applications in near-field optical microscopy and array-based optical trapping.