Wait until you learn about the public restrooms!* Yes, the Romans had very different ideas about personal privacy, and levels of privacy varied widely by class. Wealthier people had access to greater levels of privacy than everyone else (especially in urban settings), except in a couple of important ways. There are lots of potential ways to address this question and I hope others have more to add, but I'll talk a bit about differing ideas of privacy as they apply to urban housing and then a bit about some of the evidence for how the public activities outside the home.

In a Roman city, you would be likely to find a few exceptionally large properties made up of multiple lots; at Pompeii, these would be things like the House of Octavius Quartio (II.2.2), House of the Faun (VI.12.2), or House of the Menander (I.10.4). You would find more large properties, the "typical" single lot townhouses; some Pompeiian examples would be the House of the Orchard (I.9.5) or House of Marcus Lucretius Fronto (V.4.a). Then you would find smaller house-workshops, or house lots that had been subdivided into multiple smaller dwellings, and the upper story apartments that became cheaper the higher they rose (alongside the cheaper building materials and danger from fire).** A typical one-lot house would have a plan with large front doors, then a narrow entrance corridor opening onto a large atrium with an open compluvium roof and a sort of office space (tablinum) at the rear. Other rooms often opened around the atrium, and houses would usually have some sort of garden (either a small open area or a peristyle courtyard with further, more private rooms opening off of it) behind the tablinum.

Ground floor townhouses were quite insulated from their surroundings, with exterior windows set high up in the wall or altogether missing, and air circulation provided through the front door and any light wells or peristyles or little gardens located within. A little bit paradoxically, their front rooms were also sort of open to the public, with the homeowner's guests and clients encouraged to enter on a daily basis. This means that the atrium would put the best face of the household forward (since these rooms also often provide archaeological evidence of household work, like loomweights from weaving, there is something of a debate about whether or not these household activities would take place in the atrium at a different time of day when the space was more private or, as I prefer, these kind of work activities played a part in a household's public presentation).

Someone living in a cramped, top story apartment would not have dependent clients, and would likely only use the space for sleeping and storage, so those dwellings, while constructed in a way that allowed for very little privacy within and between adjacent households, would be in reality less publicly accessed. The odd dynamic between public and private spaces in the Roman townhouse (of the middlingly wealthy variety) is discussed thoroughly in Andrew Wallace-Haddrill's The Social Structure of the Roman House (1988), where he links the social activities and hierarchies of household space with the rooms by conceptually placing all of the rooms on a plane formed by the two axes: public-->private and grand-->humble (so the atrium would be a public and grand space, designed to impress visitors, especially those dependent on the higher social standing of the homeowner, while the kitchen if present would be a private and humble space, unlikely to be decorated or visited by anyone outside the household). Wallace-Hadrill goes deeply into how the architecture and decorations were designed to establish firm social hierarchies, conditioning people's movements and sightlines and activities in different areas of the house.

When it comes to the daily functions--eating, hygiene, styling, exercising--more space in the house means more space available to house them. The House of the Menander (which occupied almost a whole city block by 79 CE) has a whole kitchen and bath area at the rear of the house with a separate small garden, facilities that would have enabled its presumably wealthy (and therefore, in the smallish Roman city, almost certainly socially high-profile) owner to keep a low profile and stay off the city streets if he so desired.

Now, why might he want to avoid these public spaces? We get a good idea from Seneca (writing during the reign of Nero around 40 CE while staying at the resort of Baiae, near Pompeii), who wrote a letter in which we get a glimpse of a wealthy man's perspective on the public bath and just how active and social and cacophonous it must have been.

It's pretty evocative, so I'll quote it at length from the Loeb translation: “If you want to study, quiet is not nearly as necessary as you might think. Here I am, surrounded by all kinds of noise (my lodgings overlook a bath-house). Conjure up in your imagination all the sounds that make one hate one's ears. I hear the grunts of musclemen exercising and jerking those heavy weights around; they are working hard, or pretending to. I hear their sharp hissing when they release their pent breath. If there happens to be a lazy fellow content with a simple massage I hear the slap of hand on shoulder; you can tell whether it's hitting a flat or a hollow. If a ball-player comes up and starts calling out his score, I'm done for. Add to this the racket of a cocky bastard, a thief caught in the act, and a fellow who likes the sound of his own voice in the bath, plus those who plunge into the pool with a huge splash of water. Besides those who just have loud voices, imagine the skinny armpit-hair plucker whose cries are shrill so as to draw people's attention and never stop except when he's doing his job and making someone else shriek for him. Now add the mingled cries of the drink peddler and the sellers of sausages, pastries, and hot fare, each hawking his own wares with his own particular peal.” (Seneca Letters 56.1-2).

As far as establishing a community through repeat visits and getting to know people out and about at the local popina or thermopolium, there is some evidence in form of graffiti that these "regulars" developed relationships that unfolded over time. My personal favorite played out on the wall of the Thermopolium of Prima in Pompeii (I.10.2), between two rivals in love, Successus and Severus.

"Successus, a weaver, loves the innkeeper’s slave girl named Iris. She, however, does not love him. Still he begs her to have pity on him. His rival wrote this. Goodbye”

(Answer by Successus) - “Envious one, why do you get in the way. Submit to a handsomer man and one who is being treated very wrongly and good looking”

(Answer by Severus) - “I have spoken. I have written all there is to say. You love Iris, but she does not love you”***

As you can see, this love triangle played out quite publicly, and seems to have taken place between two regulars at this little bar who had fallen for one of the barmaids. Unfortunately, we never get to hear Iris' side of the story. Another favorite standby of Pompeiian graffiti brings me back to the very beginning: there is lots and lots of discussion of defecation. There are warnings written on the outside of houses informing passers-by that they are forbidden to defecate, there are graffiti discussing bad smells, and triumphant declarations like the pronouncement on the latrine wall at Herculaneum's Casa della Gemma (Ins. Orientalis I, nr. 1) "Apollinaris, doctor of the emperor Titus, shat well here" (CIL IV.10619). Rebecca Benefiel has done a lot of work on graffiti, and I'll cite one of her books here.****

From these, we can understand that while bathroom functions were certainly not taboo to talk about, and commonly took place in public settings, there were limits on what the Romans were willing to put up with from their neighbors. I could go on, but feel like this is getting long.

*There is a wonderful Mary Beard quote from one of her documentary series, Meet the Romans, where she sits on an Ostian multi-seat toilet and says "This is how we have to imagine the ancient city: everyone shitting together. Tunics up, togas up, trousers down, chatting as they went."

**The apartment-block style and very high insulae that grew up in longer surviving cities like Ostia and Rome took this to the extreme. Here is an amazing article with more information: Glenn R. Storey, "The "Skyscrapers" of the Ancient Roman World", Latomus, JANVIER-MARS 2003, T. 62, Fasc. 1 (JANVIER-MARS 2003), pp. 3-26, https://www.jstor.org/stable/41540040

***Translation of CIL IV 8258, 82569 from Cooley, A. and M.G.L., 2004. Pompeii: A Sourcebook. London: Routledge. (p.77-78)

****Inscriptions in the Private Sphere in the Greco-Roman World, (eds.) Rebecca Benefiel and Peter Keegan, Leiden: Brill, 2016.