Focusing light to subwavelength dimensions has been a long-standing desire in optics but has remained challenging, even with new strategies based on near-field effects, polaritons, and metamaterials. The adiabatic propagation of surface plasmon polaritons (SPP) on a conical taper as proposed theoretically has recently emerged as particularly promising to obtain a nanoconfined light source at the tip. Employing grating-coupling of SPPs onto gold tips, we demonstrate plasmonic nanofocusing into a localized excitation of approximately 20 nm in size and investigate its near- and far-field behavior. For cone angles of approximately 10-20 degrees , the breakdown of the adiabatic propagation conditions is found to be localized at or near the apex region with approximately 10 nm radius. Despite an asymmetric side-on SPP excitation, the apex far-field emission with axial polarization characteristics representing a radially symmetric SPP mode in the nanofocus confirms that the conical tip acts as an effective mode filter with only the fundamental radially symmetric TM mode (m = 0) propagating to the apex. We demonstrate the use of these tips as a source for nearly background-free scattering-type scanning near-field optical microscopy (s-SNOM).