These days I've been gravitating towards J-rock for musical.. Background noise. Not the same as having it inspire me directly, but it keeps me in the writing mood. My current work in progress is somewhat anime influenced, so it's pretty fitting to have that be the soundscape I work with.
It's also not as distracting as the normal metal stuff I'd listen to where I'm forced to listen to instrumental versions otherwise I start screaming or playing along lol
Itsue, Ling Tosite Sigure, and Sokoninaru are my go-to bands for this in order of increasingly complicated compositions. I just like atmospheric or chaotic sounds, the amount of expression is at the heart of both ends of the spectrum.
Examples of each band~
Uhh.. Sometimes I also listen to anime and gaming soundtracks to keep me in the mood, but not nearly as much as I do with J-rock and metal lol