We describe a method to map the standing-wave pattern inside an open-access Fabry-Perot optical cavity with sub-wavelength resolution by perturbing it with a commercially available tapered fiber. The method is applied to a fiber Fabry-Perot microcavity. We demonstrate its use in determining the relative position of the antinodes at two different wavelengths. In addition, we use the tapered optical fiber as a point-like source, allowing precise positioning of a microscope objective with respect to the cavity mode.