I saw someone mentioned Mellon Collie and the Infinite Sadness by The Smashing Pumpkins. If you haven't listened to that album all the way through, I'd say that would be my top recommendation. Others include Ferment by Catherine Wheel and Casanova Snake by Thee Michelle Gun Elephant. The latter band is actually Japanese, and were fairly big back in the 90's and early 2000's before they broke up. It's a great guitar record, some real nice solos on there too.
Don't all have to be classic, there are a few "future classics" from the 2000s (and some 90s sprinkled in)...
The Hold Steady - Spearation Sunday
The Mars Volta - De-loused in the Comatorium
Muse - Absolution
Elliott Smith - Either/Or
Elliott Smith - From a Basement On the Hill
...And you Will Know Us By the Trail of Dead - Source Tags & Codes
Plus, check out:
And I know it's not new to you, but channel some Nirvana. Those GP boots of the Nirvana covers are killer.
The biggest one slipped my mind somehow: Silverchair's Diorama and Young Modern. Yes, the same kids who did those post grunge albums about fifteen years ago. They couldn't sound more different now. Our Lady Peace are great, this is amazing.
Van Dyke Parks worked with them on these albums and said he hasn't heard stuff like this since he worked with Brian Wilson in the 60s. Two of my favorite albums of the last few decades - they sound like nothing else out there, really.