There were certainly guesthouses in Ireland in this era, in the broad sense of places in which you could go to drink - and indeed, get drunk. However, they weren't taverns in the English sense.

The first thing to say that that these are 599 eventful years in Ireland. They include the arrival of Viking raiders, traders and settlers in the early 800s (although 'settlers' isn't really accurate until the 840s), and the arrival of the Normans in 1169, which is often termed an invasion. So there are many possibilities for tavern-like establishments there across three different cultures.

One of the forms of this that lasts through the period was more event than establishment; the tech midchúarta, which is usually translated as 'mead-hall'. This was an event "not only of aristocratic consumption, but also of aristorcratic expenditure" (O'Sullivan, 2004, p. 85), wherein the king (and Ireland had a good few kings) could show off his generousity, that being one of the required characteristics of the nobility. So you couldn't turn up, pay for drink, and get drunk, but you could turn up, and if you were of the right rank, or a follower of the right noble, or possessed of 'an art or trade', you could get drunk and be well-fed at the king's expense. The Críth Gablach, a law text, says that a king who couldn't provide beer every Sunday was not a suitable ruler. This was also referred to as the "king's alehouse" in other texts.

These events had a fairly complex set of rules. Where you could be seated was dependent on rank, and people were very sensitive to signifiers of it. Music was required, but so was story-telling, and guests had to be silent while a recital was in progress. The food you got was also rank-dependent, and set out fairly precisely in law. There are even diagrams in the 12th-century Book of Leinster and the 14th-century Yellow Book of Lecan which set out where people were to be seated in relation to the king, with a meat-spit (most likely pork, and from the assignment of foods to ranks, probably a whole pig) and a vat of ale. Contraventions of these laws of food and placement were taken very seriously, and the Battle of Mag Rath stemmed from an incident where Congal Cláen, a king of the northern Ulaid, was mis-seated at an alehouse, and given a hen's egg rather than that of a goose. To be fair, his hen's egg came on a wooden plate, while all his peers got their goose eggs on silver, so it was probably a deliberate slight. For this reason, though, weapons were not permitted in such banqueting halls.

In the later medieval era, this principle extended to all nobles, and in less clearly marked events. It essentially became the duty of the nobility to provide hospitality to travellers. Poems were written praising the generousity of those who did so - and satires describing those who failed to. There's a sixteenth-century poem which says of one of the royal residences in Connacht that it was an open guesthouse with five roads leading to it. And this was not a grudging dole of bread and ale, as might have been the case in the estates of other countries of the era; it was a full-on celebration, in which the guests were fed in a hall decorated with hides and satin cloth and tapestries, and perhaps a weapons rack (out of reach) over the head of the host, with woolen rugs underfoot (or possibly being used to pad wooden benches), which sat alongside long tables. Mead and ale were still common here, and from the late 14th century, whisky was also served, and there is mention of red wine in the 16th. Drinking horns, goblets and 'vessels' (possibly more bowl than cup) were in use to serve these.

Aside from these noble drinking halls, there were also dedicated guesthouses, run by people with the rank called briugu in Old and Early Middle Irish, and brughaidh in Late Middle and Early Modern Irish. These were people with duties again mandated by law, whose houses were built at the intersections of roads to cater to travellers. They were supposed to be unarmed, or at the most to have a walking stick, which was intended to convey their duty to accommodate everyone without animosity, and they often served as negotiators, or offered their guesthouses as neutral ground.

An important detail of these guesthouses is that it did not cost a traveller anything to stay there. They were funded by the gifts of the nobility, and by the good farming practices of their owners. Facilities offered sometimes included baths (highest ranking guests got them first, and it looks like lower ranking guests used the same water), the washing and combing of hair, the strewing of fresh reeds and grasses on the floors, bedding (on something called a couch-bed, possibly used for seating in daytime and sleeping at night), furnished with feather mattresses, quilts and pillows, and something called a high or lofty bed, which might be something like a bunkbed or a raised platform - possibly a bed on a partial loft over the hall.

There's very little archaeological evidence to indicate that a given place was a guesthouse rather than a noble dwelling - and as above, there may not have been a lot of difference in practice. But there's a plenitude of documentary evidence in books, annals, etc. The book by Catherine Marie O'Sullivan listed below is particularly good for this information, and contains much much more than I can recount here; I recommend it highly.

Sources:

Catherine Marie O'Sullivan, Hospitality in Medieval Ireland 900-1500 (2004)

Margaret Murphy and Matthew Stout, Agriculture and Settlement in Ireland (2015)