u/Reanimator138

Before you read the list please note: some of the places are cannon. Some are mentioned in Tolkien’s writing. Some are made up for RPGs. I’ve not added anything myself, only what I found on the internet searches.

The Prancing Pony
Located in Bree and run by the innkeeper Barliman Butterbur, it is a key gathering place for hobbits. Butterbur, a jovial but famously flustered Man, he is known for his hospitality and notoriously bad memory. He inherited the inn from his father, Barney Butterbur, and manages it with the help of his two Hobbit employees, Bob and Nob. The main building has three-storys and the north wing has ground-floor rooms built specifically with hobbit-sized guests in mind.

The Green Dragon Inn
The inn is located on the Hobbiton side of Bywater, and run by Lily Cotton. It serves as a central meeting place for Hobbits to enjoy a pint, smoke pipe-weed, swap gossip, and sing traditional songs. The Inn is central to the Shire, importing exclusive ales from across all four farthings, including from Oatbarton and the Golden Perch in Stock.

The Ivy Bush Inn
A modest two-story inn located on the Bywater road in Hobbiton. The Green Dragon is on the other side of the market. A major meeting place for hobbits from both Hobbiton and Bywater to drink beer, share local gossip, and tell stories. Regulars included Daddy Twofoot, Old Noakes, and Sandyman the miller. One of its usual patrons was Hamfast Gamgee, more commonly known as "the Gaffer".

The Golden Perch Inn
Located in Stock, north of Bucklebury near the eastern borders of the Shire. Owned by Gunderic Grubb, it's said to have the best beer in Eastfarthing. The Inn is situated where main roads meet and close to the Brandywine Bridge, this is a busy Inn which is full of locals as well as queer strangers. Here weary travellers can indulge in good food and drink; probably fresh fish from the nearby Brandywine river.

The Bridge Inn
A popular establishment located on the western side of the Brandywine Bridge in the Shire. It served as a vital resting spot for travelers on the Great East Road, directly bordering the region of Buckland. 

The Floating Log
Located along the Great East Road in Frogmorton, a village in the shire's Eastfarthing. Travellers can purchase ales, food, and crafting supplies from the innkeeper, Ponto Hopsbloom.

The Forsaken Inn
Formerly known as the Last Inn, it was located on the East Road where it approaches the old borders of the Bree-land. The proprietor was said to be Anlaf the Forlorn. Dwarves and Rangers were the main patrons for the inn, and maybe some Elves. Other Men would have been very rare. And an extremely unusual Hobbit seeking adventure might have stopped by. Serving the signature ale, the beer was said to resemble grog of widely varying strength and quality. It also featured Forsaken Cider. It was later abandoned and fell in to ruin.

The All-Welcome Inn
Located west of Frogmorton, where the Northway meets the East Road. Because it sat on major trading and traveling routes, it was built to accommodate both Hobbits and larger travelers ("Big Folk") and Dwarves who passed through Middle-earth.

The Kings' Way
Cosy inn located in Waymeet. A popular eating and drinking establishment where hobbits gather.

The Fair Weather Inn
A well-known establishment situated in the town of Michel Delving, the chief town of the Westfarthing in the Shire. Serves as a primary gathering, resting, and social hub for Hobbits going about their daily business in the Westfarthing.

The Diggs Tavern
Located in Michel Delving. A traditional Hobbit tavern catering to the locals of the Shire's largest township.

The Thirsty Fox
This is a lesser-known, specific drinking establishment historically located at Greenholm, on the western borders of the Shire.

The Hammer and Tong Inn
Located at Oatbarton that is run by the wife of the local blacksmith. 

The Rabbit Hole
A tavern in Greenfields.

The Lamplighter Inn
a modest, cozy tavern located in the village of Staddle.

The Old Ropewalk
Located in Tighfield, a village in the Westfarthing of the shire, 20 miles west of Nobottle.

The Quoit and Pole
Dug close to the Three Farthing Stone, next to the field south of the Road where the mid June Quoit throwing contests are held.

The Pipe and Jug
A lesser-known tavern and inn located within The Shire.

The Mad Badger Inn
A tavern located just north of Bree.

The Bounders End
Located in Dwaling.