Originally Posted by Bob le Samourai

I'm looking for rock music that has a transcendental or dreamlike quality but is edgier and more grounded in rock than, say, shoegaze. Maybe a bit melancholic.

A few start-off points:
The Wrens - Everyone Choose Sides
Sonic Youth - Schizophrenia
Reckoning-era REM
Guided by Voices - Weedking
U2 - Bad
The Walkmen - Wake Up
Talk Talk - Ascension Day
Mew - Wherever