Sorry if the question is impossible to answer, I appreciate that tavern-keepers didn't leave extensive diaries, let alone ones that have survived for 2,000 years.
I'm less concerned with the exact example of tavern-keeper, that was just the example that I picked of a mid-ranking citizen in order to get a concrete picture of the concerns that a citizen might have had.
If it helps you could pretend that the tavern is near the docks, that I grew up in Ephesus (maybe my Dad owned the tavern before me?). I'm not a Roman citizen. I have no slaves, but a wife and two surviving young adult sons (praise Artemis after the four that we miscarried or died in infancy). My sons work in the tavern with me.
Perhaps the question is not verifiable enough? I'm trying to understand life as a citizen back then and that's fairly hard to fact-check!
Well, I suppose the sort of things people in a similar position worry about today. A tavern owner would probably be leasing the building from the owner of the insula block, and so would need to make enough money to pay that off, along with food and other things. A particularly succesful tavern owner might be able to send their son off to get educated as a barrister (that is, a common lawyer as opposed to an orator/advocate like Cicero). They might also support a particular candidate in local elections. I guess there were some other worries about plague and famine that an ancient tavern owner might have that modern ones don't, but all in all the concerns would be largely similar.
To go along with /u/Tiako ‘s answers I can give a bit more information about life in Ephesus.
Most likely you would have been intimately involved in the guild of tavern-keepers. These are often described as ancient trade unions, but in reality they were involved in almost all aspects of your life.
When you went to a public festival, like at the Temple of Artemis, you and your family would probably participate along with all the other members of the tavern-keepers guild. When you needed to go to the public latrine, you would use seats specifically reserved for your guild. One public latrine excavated in Ephesus had pillars marking which seats were maintained by different guilds – the basket-weavers, the bakers, a particular neighbourhood association and so on. When you died, the guild would probably pay for your funeral (although there were also guilds or organisations specifically for that purpose if your own guild did not provide that service).
The guild was also involved in public life. Here’s an example from the bakers’ guild in Ephesus. At one point there was a shortage of grain and people blamed the bakers. Of course, the bakers simply baked the bread and didn’t control the grain supply and were quite pissed at being blamed for the shortage. They threatened to go on strike or take some other concerted action.
Even though the authorities acknowledged that the bakers were not responsible for the grain shortage, they simply could not allow them to threaten to strike. The food supply was all-important in ancient urban life. They therefore broke up the bakers’ guild for a period of time and decreed that if they did try to strike or organise then all the bakers would be branded upon the foot.
These guilds had a lot of power. Trajan was famously leery of them for this reason in a letter to Pliny. We also know about the silversmith guild in Ephesus from the Bible, who made images for religious pilgrims and were not a fan of Saint Paul who could take business away from them. The silversmiths caused quite a bit of social unrest, which is an indication of how powerful a guild was.
It is also possible you would be a fan of the gladiators. If not a fan, you would undoubtedly hear a lot about them from your customers. Much of what we know of gladiators comes from the gladiator graveyard in Ephesus. Perhaps you were so involved in the games you would make curses on lead sheets and bury them. These cursed the opponent of your favourite gladiator, calling upon various gods or dark powers to strike them down, often with very specific directions.
Besides gladiatorial games, your leisure time might involve the theatre or the baths, which was a major focus of social activities. You might also go visit one of the two agoras, or forums. It has been suggested the lower agora was more for commercial activities (perhaps you would meet your suppliers there?) while the higher one was for politics (maybe you would meet your guild there to petition the authorities for something?).
Maybe you would even visit the local brothel. One particular building in Ephesus was long labelled as a brothel, but more recently archaeologists have doubted this label. Still, there were undoubtedly brothels in the city.
You mentioned seasonal fluctuations in your business as tavern-owner. Besides traders, you might be interested in the schedule of the Roman proconsul. Ephesus was the centre of an assize district, and the proconsul would travel around the province of Asia to take care of local matters. There would be a fair number of people travelling with the proconsul, so it is conceivable you would see a jump in business whenever they were in town.
Another seasonal fluctuation you would be interested in would involve local festivals. The Artesimon, or annual festival for Artemis would probably be your busiest time of the year. The temple of Artemis was a major attraction for pilgrims and a tavern owner would most likely have a lot of business at that time.
I happen to be quite interested in the Roman East and a lot of information comes from Ephesus, so if you have any other specific questions about life in the city I'll try to answer.