I think musical instruments are a good way to get into DIY electronics, for those interested in both of those things.
Examples include fixing or completely re-wiring the electronics in an electric guitar, fixing or building guitar effects pedals, building midi-actuated devices, building a strobe tuner, adding pickups to acoustic instruments like guitars, cellos, and violins, modding a 3-head tape recorder into a tape delay unit, building pickup pre-amps, winding guitar pickups, fixing or modding old synthesizers or divide-down organs, building new midi interfaces, getting into modular synthesis, building oscillators, filters, sequencers, etc...
Music seems to be the sort of domain where there's always some electronic device you wish you had that would make your life a little bit better in some way, and it often happens that the thing you want is something that no one currently sells, or not for a price you're willing to pay.