Ok, so alternative rock isn't much of an "alternative" these days. Sure. But there are still some strange noises being made -- and a lot of obscure sub-genres and classic used-to-be-alternative movements that have that "miles from radio" sound you're looking for. (You are.)
Below is a brief guide to ten such genres/styles/sounds. Check them out. Maybe the next time you get sick of the radio you can start your own alternative genre revival based on one or the other.
1. Grunge
Why grunge? Yeah, good question. If there is one alt rock genre more well-known than grunge, I haven't heard of it. (And thus it couldn't be more well-known than grunge -- zing!)
But this is now, folks. Yesteryear, it was different. Seriously, this genre is vintage alt-ness, especially if you unearth the original practitioners (Mudhoney, Mother Love Bone, Green River, late Black Flag, anyone?). Those babies sure feel like an alternative to something.
2. Britpop
For every American action, there is an equal British reaction. Or so the Britpopers of the early '90s would have us believe. When Nirvana led a Yankee invasion of British radio waves, UK pop added "Brit" as a prefix -- and thus a by-definition "alternative" genre was born.
Musically heterogeneous, but nationally homogeneous, Oasis, Blur, Suede, Elastica, Supergrass and many others recorded a flurry of albums that are worth revisiting -- even if only as an alternative to the above alternatives.
3. Riot Grrrl
For every male action, there is an equal female...oh, wait. I already used that lead.
When Seattle, WA was mid-birth with Grunge, the smaller-but-just-as-musically-rich Olympia, WA was brewing its own alternative -- only they mixed theirs with feminist political protest and an anti-establishment punk ethos.
Riot Grrrl, typified by articulate and aggressive bands like Bikini Kill, Bratmobile, L7, Huggy Bear and CWA, made up a bona fide underground movement that is definitely worth re-checking out.
4. Garage Rock
Garage rock originated in the mid-1960s when small-town American bands began to imitate Brit-invaders (like The Animals) with under-produced yet catchy results.
The genre's signature scratchy sound reemerged in the mid-1970s (cf. The Ramones), in the early 1980s (eg. The Fuzztones), in the late 1980s (ie. The Sonics), in the late 1990s (see The (International) Noise Conspiracy) and again in the early 2000s with The Strokes and The White Stripes.
Surprisingly, the band The The does not play garage rock.
5. Shoegaze
Characterized by a propensity to stare down sullenly at their shoes while playing -- and by a sound that inspired fans to stare in a similar fashion while listening -- shoegaze was an anti-punk, anti-grunge genre born in Southern England in the late 1980s.
Shoegaze bands, like My Bloody Valentine and Ride, amped thick, wall-like guitar sounds over the more typically featured vocal melodies, consequently challenging a number of alt rock conventions (some even before they were conventional).
6. New Wave
When new wave bands like Talking Heads, Blondie, Devo and Elvis Costello started out, their music was a less aggressive, pop-infused alternative to the straight-up punk of the day. It was so catchy, it became the first style embraced by MTV.
These days, their punky, synth-infused sounds are the stylistic grandparents to today's catchiest in indie and alt: from the devotedly retro The Faint to the fashionably devoted Interpol (and back again to Elvis Costello who, yes, is still around).
7. Math Rock
Math rock offers an antidote to my father's greatest complaint about indie/alt music: it all sounds the same. Practitioners are known for injecting traditional rock songs with off-kilter time signatures, complex harmonies and quickly-shifting song structures.
Often, as with math rock masters Don Caballero, lyrics are underemphasized. Always, however, an angular energy infects the tunes -- of bands like Q and Not U, Big Bear and Drive Like Jehu -- which rock harder than pre-Algebra ever did.
8. Noise Rock
Speaking of my father, noise rock is not his favorite genre. Why? It's loud. (Louder than punk rock). It's messy. (More-so than my childhood room). It's discordant. (Not like smooth jazz).
Inspired by the sonic intensity of 1980s punk rock, some noise rock artists (like Arab on Radar and Deerhoof) play jarring pop. Others just make jarring noise, literally (like The Locust and Anal C*nt).
Both offer the logical extension of punk's strident energy and cacophonous sound.
9. Post-rock
Post-rock is rock music. It really is. The instruments: guitar, drums, electric bass. The attitude: left-leaning, DIY, indie-based. The sound: lush, orchestral, contemplative, dynamically complex. OK, maybe it doesn't sound like rock music -- but it's definitely an alternative.
From the soft-loud-soft builds of Mogwai to the stark ambience of Sigor Rós, this genre uses the nuts and bolts of alt rock to build entirely different kinds of structures. Ones that rock (just very slowly).
10. New Folk
Also called Baroque Pop, Twee Pop, Freak Folk and anti-Folk, this genre is itself a revival of the 1960s folk movement which itself was a popularization of traditional, local music "by and for the common folk."
Or something.
These days, it's one of indie rock's most adventurous and prolific genres, featuring the lush orchestrations of Sufjan Stevens, the swashbuckling storyboards of The Decembrists, Joanna Newsom's harp yodels and Regina Spektor's lo-fi Bjork impressions.
Really though. It's good.