Deeds
I have been able to find one deed so far. You must drink 23 unique varieties of wine/beer/ale. You will primarily find these from Tavern Keep NPC's, but you will also find a few from two Vinter NPC's.
Your reward for completion is 1,200 rep points and the title "Inn League Sage of Fine Spirits"
The deed should activate and appear in your log when you drink your first one, although it also seems to appear at some point during the initial drinking quest (possibly if you drink a certain type of ale/cider??)
Here are the locations of the unique brews:

Shire
Brockenborings (The Plough and Stars)
Stock (The Golden Perch)
Frogmorton (The Floating Log)
Bywater (The Green Dragon)
Hobbiton (The Ivy Bush)
Michel Delving (Bird & Baby Inn)

Bree-Land
Bree (The Prancing Pony)
Combe (The Combe & Wattle Inn)

Lone-Lands
The Forsaken Inn

Trollshaws
Rivendell (The Last Homely House)*

Ered Luin
Celondim (Just NE of the stable)*
Thorin's Hall (?i forgot the name of this inn?)

* indicates a Vinter NPC instead of a Tavern Keep

Quests
You can find quest bestowers throughout Eriador that are associated with the Inn League (Inn League Member displays under their name). All of these quests seem to be fetching quests where they ask you to obtain a specific brew from a specific Inn within 1 hour. None of them seem to be repeatable. Here is the info I have been able to obtain thus far.

Quest: All But the Cider
Location: Brockenborings (Shire)
Bestower: Foxglove Grubb
Detail: Just down the hill from the Inn there is an Inn League Member seeking the Stars of Old cider from the Prancing Pony.
Rep reward: 500

Quest: A Bit of Brown
Location: Oatbarton (Shire/Evendim)
Bestower: Harigar Mudbottom
Detail: Just north of the stables. He wants Blagrove's Brown from the Bird & Baby Inn.
Reward: 300

Quest: One Drink Too Many
Location: Thrasi's Lodge (Ered Luin)
Quest Giver: Alrek
Detail: This is the hunter lodge SE of Gondamon and NW of Duillond. He is seeking a Forsaken Ale from the Forsaken Inn.
Reward: 700

Quest: A Reminder of Rivendell
Location: Refuge of Edhelion (Ered Luin)
Quest Giver: Lendasil
Detail: Lendasil can be found at the top of the stairs where the building colapses in the beginning of the Elf starter quest. She is seeking Dorwinion White from The Last Homely House
Reward: 900

Quest: A Member in Need
Location: Othrikar (North Downs)
Quest Giver: Muli
Detail: He wants Bombur's Beard Lager from Thorin's Hall
Reward: 700

Quest: A Drink of the Worst Character
Location: Aughaire (Angmar)
Quest Giver: Nathalan
Detail: Collect a mug of Swill from the Forsaken Inn
Reward: 900

Quest: A Dark Day
Location: Zigilgund (Forochel)
Quest Giver: Lofi
Detail: Collect a mug of Moor-boar Beer from the Prancing Pony
Reward: 700

Quest: Never Far From Home
Location: Thornley's Work Site (Bree-Land)
Bestower: Wesley Hopwood
Detail: There is an Inn League Member seeking the Limael's Vintage from the Celondim.
Rep reward: 500

Quest: A Simple Wine
Location: Echad Candelleth (Tal Bruinen, Trollshaws)
Bestower: Saerthuithel
Detail: There is an Inn League Member seeking Brandy Wine from the Golden Perch in the Shire.
Rep reward: 900

Quest: Atli's Favourite
Location: Hrimbarg (Between the Northern & Southern High Pass in the MM)
Bestower: Oli
Detail: Oli is seeking Beakbreaker Ale from the Combe & Wattle Inn in Bree-Land
Rep Reward: 900

Quest: Quite a Pickle
Location: Ost Haer in Harloeg (Lone Lands)
Bestower: Wald Mugwort
Detail: Wald wants Thistlebelly Brew from the Ivy Bush in Hobbiton
Rep Reward: 700

Notes of interest
To make the questing easier, it would make sense to purchase the brews you will need for the quests ahead of time; say, while you're completing your deed.
Here is the list of brews/ales/wines/ciders/etc you'll want to have on hand when you do your questing. As more quests are discovered I will add to this list as well.
(remember, if you're doing your deed at the same time, you'll need to purchase the following items twice so you can drink one and save one)

Prancing Pony
Moor-boar Beer
Stars of Old

Combe & Wattle Inn
Beakbreaker Ale

Thorin's Hall Inn
Bombur's Beard Lager

Celondim
Limael's Vintage

Bird & Baby Inn
Blagrove's Brown

Ivy Bush
Thistlebelly Brew

Golden Perch
Brandy Wine

Forsaken Inn
Swill
Forsaken Ale

The Last Homely House
Dorwinion White

Quest: Atli's Favourite
Location: Hrimbarg (Between the Northern & Southern High Pass in the MM)
Bestower: Oli
Detail: Oli is seeking Beakbreaker Ale from the Combe & Wattle Inn in Bree-Land
Rep Reward: 900

Found another!

Quest: Quite a Pickle
Location: Ost Haer in Harloeg (Lone Lands)
Bestower: Wald Mugwort
Detail: Wald wants Thistlebelly Brew from the Ivy Bush in Hobbiton
Rep Reward: 700