The quasi-optical propagation of millimeter-wave signals enables high-accuracy localization algorithms that employ geometric approaches or machine learning models. However, most algorithms require information on the indoor environment, may entail the collection of large training datasets, or bear an infeasible computational burden for commercial off-the-shelf (COTS) devices. In this work, we propose to use tiny neural networks (NNs) to learn the relationship between angle difference-of-arrival (ADoA) measurements and locations of a receiver in an indoor environment. To relieve training data collection efforts, we resort to a self-supervised approach by bootstrapping the training of our neural network through location estimates obtained from a state-of-the-art localization algorithm. We evaluate our scheme via mmWave measurements from indoor 60-GHz double-directional channel sounding. We process the measurements to yield dominant multipath components, use the corresponding angles to compute ADoA values, and finally obtain location fixes. Results show that the tiny NN achieves sub-meter errors in 74\% of the cases, thus performing as good as or even better than the state-of-the-art algorithm, with significantly lower computational complexity.