The Tack, Harness, and Drawn Vehicles Table gives the cost of stabling a mount as 5sp per day.
Take a look at the descriptions of the Lifestyles in the Lifestyle Expenses section of the PHB. In particular, look at the jump between Modest and Comfortable (emphases mine).
Modest. A modest lifestyle keeps you out of the slums and ensures that you can maintain your equipment. You live in an older part of town, renting a room in a boarding house, inn, or temple. You don’t go hungry or thirsty, and your living conditions are clean, if simple. Ordinary people living modest lifestyles include soldiers with families, laborers, students, priests, hedge wizards, and the like.
Comfortable. Choosing a comfortable lifestyle means that you can afford nicer clothing and can easily maintain your equipment. You live in a small cottage in a middle-class neighborhood or in a private room at a fine inn. You associate with merchants, skilled tradespeople, and military officers.
These descriptions, in my opinion, indicate that choosing a modest lifestyle means you would need to find and pay for stabling for your mounts and beasts of burden separately, whereas choosing a comfortable lifestyle means accommodations for such animals can assumed to be included in your lifestyle. A day laborer would not have a mount, nor would his boarding house have an attached stable. A military officer would have a mount, a merchant would have either a mount or beast of burden, and there would be facilities for these at their homes (or places of work, if they were different)
Rules-free quasi-medieval verisimilitude
A low quality inn might not have a stable at all. If it did, it might just be a fenced yard with no roof.
A high quality inn likely has a stable with individual stalls.
Inns cater to travelers and often have attached stables. There is unlikely to be a stables independent of such a business, that is, a place whose sole income comes from boarding mounts, simply because the income from such an enterprise would not justify the expense of the land occupied in a city. An exception might be nearby a sports arena or hippodrome, riding course for the wealthy, permanent cavalry encampment, etc.
Along trade routes there are likely to be stockyards unattached to inns where you could board beasts of burden like your cargo mule.