We present a procedure for fabricating optical tips from photonic crystal fibers which feature a solid core surrounded by a cladding with a hexagonal, multilayer arrangement of air channels running along the length of the fiber. Such optical tips may have unique advantages for the production of near-field optical aperture probes (i.e., metal-coated optical tips with a subwavelength aperture at the tip apex). With both cladding and core made of pure silica, these fibers are fluorescence-free; they support only a single mode over a broad wavelength range (covering the visible and near-infrared spectrum), which makes them useful for multicolor experiments; and they exhibit zero group velocity dispersion at visible wavelengths, which opens up the possibility of femtosecond applications in the near field. Our tip fabrication procedure leads to a sharp, protruding, central tip formed exclusively from the fiber core amidst a regular arrangement of smaller tips from the inner, microstructured region of the cladding. A mechanism for tip formation is proposed based on optical observations at various stages, which explains the self-centering nature of the process.