Sparta and the Mars Volta are both split-offs from ATDI. Sparta is much more conventional. TMV is some prog-rock shit.
I loved TMV's first album, the new one isn't really doing it for me, though. I'm trying, though. I'm going to see them next month, looking forward to it - I've heard the show is nuts.
Radiohead - everyone should like them, imo. The Bends, OK Computer, Kid A - if you can't find anything you can like on either three of those albums, I dunno what to tell you.
The Strokes, I like.
Last punk album I heard was The Evens' 12 Songs. If you weren't aware, the Evens is Ian McKaye's side projec to keep him busy while Fugazi's on hiatus. The album's very restrained, has an unplugged feel to it, I guess. I'll probably end up buying it, since Dischord is the epitome of non-shadiness.
As for as rock goes, albums this year that I'm listening to:
Bloc Party - Silent Alarm
Bright Eyes - I'm Wide Awake, It's Morning
The Evens - 12 Songs
Iron & Wine - Woman King
Kings of Leon - Aha Shake Heartbreak
I have a lot of Killers songs stuck in my head, but haven't actually played them since after their show last fall.