IMO, looking at your interests, the Wild Atlantic Way and in particular the north-west might be of interest to you. It is less touristy in the north-west and more rugged but I have done any walks up there. Search the Irish Times newspaper for 'walks' and it will pop a regular feature they have in their weekend paper - I've done a couple and their good. Other walks? There a couple of good ones at Glendalough which can be a day trip from Dublin and Howth, again near Dublin. An iconic Irish walk is Croagh Patrick which is a religious pilgrimage for some but more a test of endurance involving scrambling over loose shale towards the peak (and coming down is worse).
IN Dublin, in terms of museums and buildings, I recommend Chester Beatty Library, Marsh's Library, St Michan's Church (check website for vault tour times as this is the main reason for visiting), and The Four Courts (you can' take pix but it is a nice piece of architecture and history).
In terms of sports you are deep into GAA season of hurling and gaelic football. I think you'd be best off looking to see a local game. I follow a football team called Corofin who play in Tuam and its great to watch. There is no drinking at these games.
Places for drinks? The country is crawling with them. In Dublin I recommend O'Donoghues in Merrion Row near St Stephen's Green, The Cobblestone in Smithfield, Dawson's in Dawson St, McNiells in Capel St, and Keogh's off Grafton St. For local ales try The Black Sheep in Capel St.
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I am of the opinion that Dublin needs a good solid two days. One centring around the west end and sights like the modern art museum, St Michan's Church (check online for tour times as a tour of the vault is a key part of the visit), the Guinness Storehouse, Kilmanhaim jail, Phoenix Park/zoo (the zoo is the 2nd oldest in western Europe and has a very strong breeding programme with lots of newborns) and Collin's Barracks (more likely a selection of).
The second day centrally to include the national gallery, Merrion Square, the Kildare St archaeology museum, Chester Beatty Library, Trinity College/Book of Kells, Temple Bar, Grafton St and St Stephen's Green. IMO, the Guinness factory and the Book of Kells are not worth it (particularly price wise) but visitors seem to come away satisfied from visits to both.
St Patrick's, Marsh''s Library and Christ's Church Cathedrals are between these two 'sections' of the city and can be done in either.