It's not very clear what you're asking.

Inns were originally places for travelers to stay when on the road, they were not gathering places. In that sense, inns are very old in India, dating at least to the time of Chandragupta Maurya (around 300 BC), who built the Grand Trunk Road. It stretched the entire breadth of his empire, from Kabul in Afghanistan to Patliputra in eastern India. There were inns along the road for travelers to stop for the night, rest and resupply.

This system of travelers inns (called "serai" or "caravanserai") later extended pretty much over all of north India, and probably south India as well, though I am less familiar with that. Even today there are dozens of towns across India and Pakistan with names reflecting their origins as serai: Mughalserai, Yusuf Serai, Jia Serai, Serai Mir, Serai Alamgir, Serai Rohilla, Serai Khas, Chaga Serai. And lots more.

A serai was basically a walled compound, walled for protection from bandits and wild animals. Inside were several buildings and a courtyard - stables, wheelwright, blacksmith, general store, inn with food and beds, etc.

As for "gathering places" in the sense of the local neighborhood pub where you might go of an evening after work, they are pretty recent, not just in India, but in most places around the world. Pubs or bars were not common in medieval Europe either, so far as I know. In England, typically the local alewife would put up a sign outside her door once or twice a week to let people know the beer was ready. You'd take your jug or a pot to buy some, then bring it home to drink.

If you visit Indian villages today, social gatherings are basically in people's homes, or just outside them, because of weather and light. Outdoors is cooler with the evening breeze and there is light enough to not need smelly oil lamps. Typically, they will lay out a few bamboo cots ("charpai") outside some local dignitary's home, the regulars stop by to chat, anyone else can drop in to hear the news and gossip. Women have their own separate equivalent.

In towns and cities, there were a lot of eating establishments. Not full service restaurants - more like street vendors with open kitchens facing the road and perhaps a few tables and charpais spread out in front. They served as gathering places for people to talk.

As far as drinks go, there is pretty huge variation depending on which part of India you're talking about. Tea is very popular today, but such widespread popularity is very recent, after the British East India company started growing tea in massive amounts in the northeast. But tea was locally popular long before that - there is archeological record of people in different tribes/communities drinking tea from at least the 12th century. It probably predates that, since tea is native to both India and China, and grows wild in large parts of the north and northeast.

In the north, dairy was very popular. Milk, buttermilk, lassi (a yogurt drink) were common in Punjab, UP/Uttarkhand, HP, Haryana, etc. Sugarcane juice was also extremely popular and you can still come across little mills that people set up in villages, where they crush the sugarcane through the mill and people gather around to drink the juice.

So far as alcohol goes, it was also popular in India in different times and places. The Vedas mention several alcoholic drinks, such as Kilala, which was a sweetish fermented drink possibly made from honey, or Masara, which was rice liquor (kind of like "handiya" which is still made today). The Ramayana mentions several kinds of liquors. Kautilya's Arthashastra mentions at least a dozen. Charaka (one of the originators of Ayurveda, around 800 BC) mentions 84 different alcoholic beverages. There were lots of different sources - fermented honey, rice, barley, sugar cane, tree sap (coconut and palmyra), fermented fruit juices (grape, mango, dates). Some flowers were fermented to make flower wines - Mahua, Kadamba, Dhataki.

However, I'm not aware of any mention of bars or pubs as gathering places for people to drink until more recent history. These drinks were sold in shops, and the assumption is that people bought them and took them home to drink, much like in Europe. Kautilya mentions that in his time (around the 4th century BC), there were liquor shops in most villages and janpads.

Well the Mongols set up a system for moving goods and exchanging information kind of like the pony express. This was called the Yam system. Horsemen would move good and information along this route for the Empire. The Yam riders would have a metal pendant called the Paiza that would allow them to gets food, water, and fresh horses at check points thought out the Empire usually 140 to 200 kilometers apart. I would assume that many of these locations served the public as well in the areas the Mongols controlled. and I'm sure these locals were sometimes existing taverns along traditional trade routes. Furthermore other Central Asian states mimicked this system as well like Russia which called their system the Zam. And considering the Mongols controlled large portions of Asia during the Medieval period the Yam system may have served as a tavern more much of the travelers in Central Asia. India most likely had a different system since they resisted Mongol invasion and occupation successfully.