You seem to have the same general musical taste as me, at least from those albums. If you liked Blackalicious you should try some Binary Star. My friend is a huge fan of Blackalicious, and now he loves Binary Star. I also strongly second So Much for the Afterglow, great CD.
For a sound that's pretty different from most typical rock music, try Quarashi. If you don't like it at first, just try listening to it a few times, it grows on you.
Also, for some good underground-ish hip-hop/rap, try Jedi Mind Tricks, especially the album "Violent By Design".
For some very chill but upbeat and soothing music, try Kinobe - Soundphiles.
Trip-hop/chill music/"Background music": Try the Flexistentialism CD, it's a compilation of artists, mainly DJ Food, 9 Lazy 9, The Herbaliser, etc. Also "Funkjazztical Technology", a similar compilation of the same artists.
Up until their current CD, the Ataris were my all around favorite rock band. If you're looking for upbeat, punkish but not too harsh rock, try "Anywhere But Here", the remastered album. For something closer to normal rock, try "Looking Forward to Failure" or "Blue Skies, Broken Hearts, Next Twelve Exits..."