I'm going to have to step back about five or six years for this. My taste in music used to be like yours, then I began to find really bizarre stuff fascinating. I still appreciate the old stuff, though. SO I apologize in advance if I throw in a few things that don't match your interests at all; I'm having trouble getting into the other mindset.
I second the suggestion for Brand New; that used to be my absolute favorite band.
King Crimson was formed in the late 60's; you might recognize the song "21st Century Schizoid Man" because it was poorly mixed into Kanye West's very popular song "Power" (yes, this upset me). He just had to try to ruin their good name. In the Court Of The Crimson King is one of their more accessible albums, as is Lizard. The song "Lizard" is fabulous but about 23 minutes long. Actually, this is a band that I currently love--not an old interest.
Hurt is another former favorite band, though I have to say that I was impressed by their latest album. I think "Losing" is a pretty good representation of their music.
Deftones is an obligatory suggestion - I suggest the song "Deathblow"
And a few others:
Crippled Black Phoenix - The Brain/Poznan
Cynic - Carbon Based Anatomy
Katatonia - In The White
Manchester Orchestra - Where Have You Been?
A Perfect Circle - The Outsider
The second parts of each suggestion above are songs that represent the band well enough. Sometimes I seem to stumble upon some of the worst songs produced by a particular band, assume the band is terrible, then return to it later and find that the other songs sound nothing like whatever I found.