Acoustical music

Nirvana / Their live acoustic one (MTV unplugged, I think)
Grateful Dead / Reckoning (Not completely acoustic) 
Old & in the way
Those are also all recorded well

Sarah Jarosz - all
Abigail Washburn (both with and without Bela Fleck)
Darryl Anger - "Republic of Strings"
Richard Thompson - "Acoustic Classics"
Second the Grateful Dead - "Reckoning"
"Acoustic Cafe" - a Putamayo Presents collection
"Acoustic Africa" - another Putamayo
Stuart Duncan, Yo-Yo Ma, Edgar Meyer, Chris Thile - "The Goat Rodeo Sessions"
Noam Pikelny - "Plays Kenny Baker Plays Bill Monroe"
Habib Kotie and Eric Bibb - "Brothers in Bamako"  THIS IS FANTASTIC!

Not sure which you can get on vinyl.
Best wishes

I like everything boxer12 suggested.   Also,
Hot Tuna--Live at the New Orleans House
DeLucia/McLaughlin/DiMeola--Passion, Grace and Fire
Shakti--A Handful of Beauty
Chieftains--Chieftains 9
Tony Rice--Cold on the Shoulder

I can't believe it - someone else likes Handful of Beauty too. Composition called 'India' is a masterpeace and another long cut on side B is close to it.
Also:
Dead Can Dance - Into the Labyrinth
Dead Can Dance - Toward the Within
Al Di Meola - Cielo e Terra
Paco de Lucia - Siroco ( analog recording/digital mastering, sounds closer to digital to my ear but it is his best album ).
John McLaughlin Trio - Live at Royal Festival Hall ( digital ).

Passion Grace&Fire is spectacular, all digital though. Get original Japanese pressing, I saw a few on ebay and discogs. The same for the Shakti - good analog recording and mastering.
Cielo e Terra - American or Canadian first run ( thicker vinyl ) is good. German, Dutch - NOT DMM - are good. Japanese is best, hard to find, I saw one on Discogs for $50 from Canada.
Dead Can Dance - original UK, I didn't try any reissues.
Siroco - Japanese best, saw one on Discogs from Spain, German good.