I LOVE it when bands use unconventional and exotic instruments and particularly I love it when bands use the sitar. If anyone can rec me anything including that and I end up enjoying it, I will love you forever.
Not a band, but if you love the sitar and you don't listen to the music of the Shankar family, you're seriously missing out.
Ananda Shankar is probably the most accessible as he merged traditional sitar playing with Western Influences, he plays some seriously incredible stuff.
Won't embed them if it messes up your browser, so here are some youtube links.
If you end up enjoying him, make sure you listen to his uncle, the legendary Ravi Shankar, who is more traditional, but no less amazing. He sadly died about a month ago actually.His daughter Anoushka Shankar also is a musician and definitely worth listening to as well. Ananda is probably my favourite of the three though, so start with him.
I checked out Ume as well, thanks! Yeah, they sound similar, it's pretty cool stuff. Can definitely see myself listening to this more.