The thing I love about these bands is their albums are just superb from beginning to end, these bands don't get the credit they deserve. Their albums are some of the greatest I ever heard:

Modest Mouse:
The Lonesome Crowded West
The Moon And Antarctica
This Is A Long Drive For Someone With Nothing To Think About
The Fruit That Ate Itself
Built Something Out of Nothing

Built To Spill:
There's Nothing Wrong With Love (one of my top-3 fav albums)
Perfect From Now On
Keep It Like A Secret
Their 2 latest albums Ancient Melodies Of The Future, and You In Reverse are good too if you appreciate BTS, but their first 3 albums are so good, it's pretty hard to get any better.

The Shins:
Oh, Inverted World
Chutes Too Narrows

Broken Social Scene:
You Forgot It In People
and their self-titled, amazing albums

Pavement
Slanted and Enchanted (fucking classic)
Crooked Rain, Crooked Rain
Wowee Zowee

I like Apologies To The Queen Mary by Wolf Parade, but they sound too much like Modest Mouse. I should check out Island, I'll probably like them since your tastes in music are similar to mine.

Some bands you gotta check out of you haven't already have them in your collection:

Grandaddy (in my opinion, the greatest band ever)
David Garza (The most underappreciated artist ever, check out the album This Euphoria and you'll be perplexed to why this guy isn't famous, this guy deserves to get a million of dollars)
Neutral Milk Hotel
Beulah
Bright Eyes
Elliot Smith
Apollo Sunshine
Apples In Stereo
Arab Strap
Arcade Fire
The Rapture
Afghan Whigs
Lilys
The Microphones
Mazarin
The Walkmen
Mooney Suzuki
The Wrens
Sunset Rubdown

I could go on forever listing great indie.