Dublin is dirty, noisy, and congested — all things I hate with a vile temper. But I still adore it. It overflows with the art and symbolism of pagan Ireland. All of the places described below are within easy walking distance of the O'Connell Street Bridge (called "an Lár" — "the Centre") in downtown Dublin (the places below have been listed strictly under this criteria). Most are free.

1. National Museum of Ireland, Kildare Street. One of the finest collections of prehistoric and early medieval (yet with pagan theme) artifacts in the world. The main hall, and "The Treasury" adjacent to it, contain great bronze war trumpets, brooches (including the "Tara" brooch, dating from early Christian times but fully pagan in design and arguably the "most beautiful peace of jewelry in the world"), shields, torcs, neck rings, amulets, bracelets, bowls, chalices, and other items. Hundreds of golden items bearing triskeles, knotwork, spirals. There are life-sized reproductions of carved stones and educational displays (in English agus as gaeilge) about how various different items were made and used. There are also stone-age artifacts (including the Knowth "faced maze head"), on sale in the shop daggers (called letter-openers) and torcs reproduced in bronze or silver from those in the museum's collection. Cameras are not allowed, but the artifacts are splendidly rendered on post cards available in the museum shop. There is also a coffee-shop where you can buy bottled spring water from Co. Meath close to Tara. Some days are free, on others there is a small charge. Only a small part of the museum's collections are on display in the room. It also has one of the finest collections of Maori art out side of New Zealand (with the explicit permission of the Maori themselves whose chiefs and shamans put on a dawn ritual outside the museum to bind the ties of affinity between the Maori and Irish peoples).
2. Táin Mural, immediately west of the Kilkenny Centre, just south off the sidewalk on Nassau Street. A rainbow stone mosaic in semi-impressionalist style that depicts various episodes from the Táin Bó Cuailgne. Absolutely stunning. Free.
3. Not from pagan times, but pagan enough. At Trinity College, in the "Long Room", while the centre cases are filled with a monkish colouring books, at the far end is THE Harp, the physical "Brian Ború Harp" which is the official emblem of the nation. Small entrance fee. (So, ok, while you're there you CAN see the Book of Kells too if you want, but look at the Harp first!)
4. Lir Clock, O'Connell Street. For years this ghastly mechanized art nouveau rendition of Irish myth was thankfully broken, but now some twerp has fixed it and at all hours it bongs out the silliest sing-alongs which assault the ears for blocks as princess and swans revolve high above the street. Free, bring ear-wax.
5. Vikings. There are or were or will be various displays depicting Viking times in Dublin. The locations and times change. All did or do or will charge an entrance fee.
6. Bookstores with very good offerings of ancient Irish tales in English and Irish include (in downtown area): Hodges Figgis (Dawson Street), Watertone's (Dawson), Fred Hanna (Nassau Street), and Siopa Leabhar (Harcourt Street a half block south of the SW-corner of St Stephen's Green, mainly books in Irish but the fullest line of the bilingual Irish Texts Society in Dublin). Dublin has a dozen plus other fine bookshops in the same downtown area, although their stock of pagan material is far less than the above.
7. The Death of Cúchulainn Statue, General Post Office, O'Connell Street.Ulster pagan hero tied to a standing stone with a raven on his shoulder. Is supposed to honour the martyrs of the Easter Uprising of 1916. (That the Republic would honour modern Catholic heroes who fought for a free united Ireland with a pagan Ulsterman who fought to keep Ulster separate from the rest of the country tells you a lot more than you might want to know, although if your mind-set is truly Irish, it makes perfect sense.) Free.
8. The Charioteer, Talbot Street. A statue of an ancient Irish chariot with driver (full frontal male nudity, kiddies). There is a moat with draw-bridges that are taken-up at night so go during the day. Free.
9. Garden of Remembrance, one block north of north end of O'Connell Street. A "bua" pagan power site. Only a little Christian symbolism, officially a memorial to the fallen dead, but war/death are simply not represented. Instead, it is massively and over-whelmingly in symbol and inscription a gigantic hymn of praise to the Tuatha De Danann and to druidic magic. No superlatives are too high. Free.
10. Chester Beatty Library, Ballsbridge. Not Irish pagan, but the best collection of Oriental manuscripts in the world. Also art. Mustn't touch (unless you're an accredited scholar) but there are guided tours for the public. Small entrance fee.
11. Royal Irish Academy, Dawson Street. Not open to the general public but one of the best collections of ancient Irish manuscripts in the world for the serious researcher.
12. National Library of Ireland, just across Leinster House from the National Museum. Again, you won't be admitted unless you can prove you are a serious researcher, but they often have various displays in the lobby.

Note: nothing on trees above: there are few "druid trees" in downtown Dublin, but St Stephen's Green and other places are treed. A long walk from an Lár is Phoenix Park (named not after the mythic bird but as a bilingual pun on the Irish for "bright water") which not only has trees but is large enough to support a free-ranging deer herd. There's more to Dublin than this. Non-pagan, but still impressively. at almost every turn there are mosaics, bronzes, stone-carvings of (to name just three): life sized flower-girls, monkeys playing pool, and chicken foot-prints in the sidewalk. Buskers and sidewalk artists abound. And a same-or half-day round-trip by bus will reach such sites as Tara, Tlachtga, Newgrange, Dún Ailline, the Wicklow Mountains, Drogheda, etc.).