Museum in Dublin
Kilmainham Gaol is a former prison that held many of the leaders of Irish independence movements, including those executed after the 1916 Easter Rising. Guided tours only, at a very modest price. The Victorian main hall, the exercise yards, and the execution courtyard are powerful and moving. Budget travelers book online in advance (slots fill up fast) and get one of the most important historical experiences in Ireland for less than the price of two pints.
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Other places worth the walk, and what each one costs.
The Book of Kells Exhibition at Trinity College displays the 9th-century illuminated manuscript of the four Gospels, one of the most famous medieval manuscripts in the world. Entry is paid (includes access to the Long Room, a 65-meter barrel-vaulted library of 200,000 books and marble busts).
The Chester Beatty Library in Dublin Castle is a museum of manuscripts, miniature paintings, prints, and rare books collected by Alfred Chester Beatty, an American mining magnate who made Dublin his home. Free.
Christ Church Cathedral is Dublin's oldest building (founded 1030), a medieval cathedral with a massive crypt (the largest in Britain and Ireland), the tomb of Strongbow (the Norman warlord who conquered Dublin), and a preserved cat and rat found in an organ pipe (known as "Tom and Jerry"). Entry is paid at a modest price.
Free formal gardens behind Dublin Castle featuring a Celtic knot pattern laid out in planting beds. The name recalls the "black pool" that gave Dublin its name.
Dublin Castle was the seat of British rule in Ireland for 700 years, from 1204 until Irish independence in 1922. The exterior grounds and the Chapel Royal (with spectacular carved stone and oak interiors) are free.
Glasnevin Cemetery is Ireland's national cemetery, where Michael Collins, Eamon de Valera, Daniel O'Connell, and many other figures from Irish history are buried. Free to enter (guided tours are available for a fee).
Working out what Dublin costs?
The whole of Dublin