Frequency Response Function (FRF) measurements are widely used in gravitational wave detectors, e.g., for the design of controllers, calibrating signals, and diagnosing problems with system dynamics. The aim of this paper is to present GraFIT: a toolbox that enables fast, inexpensive, and accurate identification of FRF measurements for gravitational wave detectors compared to the commonly used approaches, including common spectral analysis techniques. The toolbox builds upon recent developments in non-parametric system identification by utilizing a local modeling technique, which is particularly effective in reducing the impact of transient effects. It is furthermore designed to be user-friendly, handling systems of arbitrary input-output dimensions, and systems operating in a closed loop. The toolbox is validated on two experimental case studies of the Virgo detector, illustrating more than a factor 3 reduction in the estimated standard deviation using GraFIT for the same measurement times and comparable estimated standard deviations with up to ten times less data using GraFIT with respect to the commonly used spectral analysis method. As a result, GraFIT can reduce commissioning time and detector downtime due to noise injections, while also improving the overall quality of the measurements.