Dublin and surroundings 6 days total

Trinity Church? Or Trinity College?
Newgrange is an excellent place to visit. Older than the pyramids. Guided tours and visitor center are very well done. Could be your first stop after picking up your rental car at the airport.
Athlone has a castle on a lake, pub and nearby Clonmacnoise. I haven't been, but it's on my list.
If you decide to skip Rock of Cashel, you could do this trip without a car. All of the above can be done without a car (save, probably, Clonmacnoise). Take the train to Waterford or Cork. Great food scene and the Butter Museum in Cork, plus day trip to Cobh.
The only time I can recall seeing Irish dancing in Ireland was in 1995 when there was a summer school in, I think, Tobercurry. Here is a list of Irish music festivals (some are outside Ireland): https://www.irishmusicmagazine.com/links/tours-festivals/

Thank you!! I meant trinity college.

Newgrange is impressive for sure. We also loved Glendalough, Kenmare, Cashel. Enjoy!

Day 1: arrive in Dublin, take bus or taxi to City Center and check into hotel. See Temple Bar and Grafton Street If you are still awake you could consider the Archaeology Museum, Dublin Castle, Chester Beaty Library and Trinity College/Boof of Kells. Night 1 in Dublin.
Day 2: Howth and anything else you might want to do. Maybe the things listed above or Kilmainham Gaol. Night 2 in Dublin.
Day 3: Rise and shine early. Rent car either from the airport or Dublin City Center off the South Circular Rd (saves you from backtracking to the airport and driving on the M50). Drive to Rock of Cashel also see Hore Abbey. Drive to Kinsale. Nights 3 and 4 in Kinsale. See Charles Fort, Drive to Old Head, take the ferry to Cobh. Drive along southern coast and visit random beaches. Lots of restaurants. What's your budget?
That leaves you with one spare night that you can either spend in Kinsale or head back to Cork. Where are you going from Ireland and from which airport? If you are going to the U.S. you need to be at the airport 3 hours ahead of departure because you pre-clear U.S. immigration in Ireland. So that last night might need to be closer to the departure location.

You could take the train to Cork and rent the car there for day trips to Cashel and Kinsale.
In Cork, Sin é is a pub with traditional music most nights, if not every night. The English Market is fun to explore, and the restaurant upstairs is good for breakfast or lunch. Day trip to Cobh. I ate at Goldie, a fin-to-tail seafood restaurant. I wouldn't take teenagers there (too nice). Reservations can be made online, as I recall.

Thank you so much!

We are traveling to Spain from Ireland.
Not sure what our budget is. We like to eat well but not pay and arm and a leg 🤣
I think we need to rent a car in Dublin airport bc we are flying and taking off from Dublin.

If you haven't bought the plane tickets to Spain see if you can fly out of Cork airport. I think they do have flights to Spain. I personally don't like to be more than about an hour from my departure airport. So if Dublin is already set, I'd look into spending the last night in Trim, Malahide or Wicklow. Trim has a castle and monastic ruin. You could possibly go to the aforementioned Newgrange, or Knowth. Malahide has a manor house, is on the coast and good restaurants. In Wicklow there's Glendalough and nice trails.

Best restaurant in Kinsale is Finn's Farmcut but it's $$$. An old standby is Fishy Fishy. Both need resrervations.

We already bought the tickets. I think the last night we will stay in rock of cashel.
Thank you so much for the recommendations! If u think of anything else let me know :)

If you want Irish dancing there is a hotel on the river called The Arlington that puts on shows. It may be a little hokey but that's what being a tourist is sometimes 😄

As for castles I recommend Malahide Castle (Dublin Castle isn't great), there is a museum of curiosities, views are in Howth, good beach in Bray, for pubs there's way too many to list but the Brazen Head and Stag's Head allow under 18s. Lots of good food such as L.Mulligan Grocer (which is very to the Cobblestone pub), Bunsen or do a food tour. I talk about that in another post.

Enjoy Dublin!

While in Dublin, I highly recommend visiting Kilmainham Gaol to learn about Irish history. Tickets for your date go on sale 28 days in advance. You need to be on the site immediately when they go on sale to purchase tickets. Guided tour is the only way to visit the Gaol. Also visit the GPO Museum to learn about the Easter Uprising of 1916. Take a "free" walking tour with Yellow Umbrella Tours.

As a daytrip from Dublin, I highly recommend visiting the passage graves at Knowth and Newgrange. They are older than the Pyramids in Egypt and Stonehenge. You can enter a passage and chamber in Newgrange. It really is a special experience.

Thank you for all the responses!!! These are great!