I love love LOVE Postmodern Jukebox. Bradlee's arrangements really give new life to the song and can turn an unlistenable song to an actually decent one, or make a good song even better. My favorite is probably his klezmer arrangement of "Talk Dirty", which is in that "making a bad song good" category. Plus the Yiddish rap is fantastic. I also really like the ones they've done with Haley Reinhart and Puddles, especially their cover of Creep which is 1000% better than the original.
Speaking of, if you dig PMJ, I'd recommend
Robyn Adele Anderson. She's done a couple of songs with PMJ (like Talk Dirty), and does something similar on her channel. She focuses more on covering alternative rock songs from what I've seen.
And, one more, I'd also recommend
Metaphump. They do jazz fusion/rap covers of metal songs. The rapping has been a somewhat contentious thing, but I dig it. They've got a lot of Snarky Puppy influence, and the fantastic Camille Bertault as one of their vocalists (she does the scat solo in the song linked). They don't have quite as many videos, unfortunately.