Suggest one obsure album we all should hear

Oh boy. First, a few recommendations already made that I would second:
The Go-Betweens "16 Lovers Lane" although I'm not sure how obscure that is.

Japan: Tin Drum

The Residents: Commercial Album

Pere Ubu: The Modern Dance

Since I tend to more obscure indie type bands my recommendations will go that way:

My first and the one I would make if you threatened to kill me unless I only make one is The Raincoats: Odyshape.  This is an amazing album for the band on their second album with only one skilled musician. The songs are not the typical formula and so can be difficult. Two main writers/singers. I think the song: Shouting Out Loud is one of my all-time favorite songs but it is not an easy listen.

Thin White Rope is a really inventive great band that very few people paid attention to. All of their albums are good but the most complete is Sack Full of Silver. 

Sleater Kinney's Dig Me Out when they were getting going is an awesome album.

The Jack Rubies: See the Money in My Smile is an album I bought by accident but ended up loving. 

Another accidental purchase was Mutants: Fun Terminal. Kind of fun showy indie rock. 

I don't know if this is obscure but it is Ultravox the John Foxx version, Systems of Romance. This album caused their label to drop them prior to the Midge Ure rebirth but, it is a dang great album and who knows what would have happened if people actually recognized that. 

These are all older ones and I don't know how obscure the more recent stuff is because everything is on Spotify or something. Margaret Glaspy's Emotions and Math, Pip Blom's Boat, MIYNT's various albums (online), Crumb's Jinx, 

Obscure is SUCH a subjective matter. Some people are aware of the group Television, others aren’t. Same with The Skeletons/The Morells (same core members), a fantastic band out of Springfield, Missouri, whose fans include Dave Edmunds, Nick Lowe, Elvis Costello, and The Del-Lords (also obscure? Skeletons/Morells bassist Lou Whitney engineered and produced The Del-Lords Frontier Days album). I have all the Skeltons and Morells albums, and even saw them live. Skeletons drummer Bobby Lloyd Hicks (sadly passing away in 2017) also played in the bands of Dave Alvin and Steve Forbert.

Is Loudon Wainwright III obscure? How about Willie DeVille? Spooner Oldham? Dann Penn? Laverne Baker? Lou Ann Barton? Iris DeMent? Evan Johns? Danny Gatton? Al Anderson? Terry Adams? Mike Auldridge? John Wicks? Emitt Rhodes?

Record labels long operated by "pushing" only so many releases per fiscal quarter (their promotional budgets were not unlimited), using the other releases as tax write-offs. For every one Alison Krauss, there are a hundred Rhonda Vincent’s. For every one Rolling Stones, there are a hundred NRBQ’s. And NRBQ were/are very well known, at least amongst good musicians. I saw them live recently, and they were absolutely fantastic, far, Far, FAR better than The damned Rolling Stones. Why are people still interested in such a lame band? They stink, and have for years.

How about the great Garage Band The Lyres? Frontman/singer/Farfisa organist/songwriter Monoman (real name Jeff Conolly) is one of the greatest live performers I’ve ever seen (at Club Lingerie on Sunset Blvd.), like a Punk Jerry Lee Lewis. Legendary amongst fans of the Garage Band genre, totally unknown by, I’ll wager, everyone here. As are by most The Flamin’ Groovies, who are a much, much better live Rock ’n’ Roll band than are The Stones. Why aren’t they more well known? Do YOU own any of their albums? ;-)

Yes, of course musical taste is a huge factor. Casual music listeners have no interest in plowing the musical fields, looking for as yet unheard music. But even more serious listeners have long relied on major media to steer them towards new music. That will get you only so far; read interviews with musicians, singers, and songwriters, find out who THEY like. Following the bread crumbs back to the source also reaps great rewards. Once I had heard "Money (That’s What I Want)" by Barrett Strong, the version by The Beatles sounded like the pale imitation it is.

Most of ya’ll know of (and like, I presume) John Hiatt, but did you that know before his solo career he was member of a group named White Duck (terrible name!)? Their two albums on UNI Records are pretty hard to find, but not terribly expensive should you want to be a Hiatt completest.

Philip Cohran and The Artistic Heritage Ensemble - On The Beach

”Spritual” Jazz circa 1968. 
 

Yeah -- NRBQ. I'd forgotten how tight and fun they were.

dz13 - Yeah, I was a fan of Ultravox. I have at least three of their LPs. I'm pretty sure they're one more band I saw during my Sunset Strip night club-going days.