In spintronics, the propagation of spin-wave excitations in magnetically ordered materials can also be used to transport and process information. One of the most popular materials in this regard is the ferrimagnetic insulator yttrium iron garnet due its exceptionally small spin-wave damping parameter. While the small relaxation rate allows for large propagation length of magnetic excitations, it also leads to nonlocality of the magnetic properties. By imaging spin waves, their band structure is mapped with high-frequency resolution using a magneto-optic super-Nyquist sampling technique. In doing so, wave-vector selection is shown to suppress dispersion effects to a large extent, allowing for local measurements of spin relaxation. Moreover, we demonstrate even higher control of magnon propagation by employing the wave-vector selectivity near an avoided crossing of different spin-wave modes where the group velocity approaches zero. Here the local engineering of the dispersion allows us to construct magnonic waveguides, and at the same time it reveals the local relaxation properties.