Dublin's sights are compact and mostly walkable from the city centre. The historical core — Trinity College, Dublin Castle, Christ Church Cathedral, St Patrick's Cathedral, and Kilmainham Gaol — can be covered in two full days. The National Museum of Ireland (archaeology) and the National Gallery are both free and excellent; together they make an easy half-day.
The Guinness Storehouse at St James's Gate is the most popular paid attraction in Ireland — the self-guided tour ends with a pint in the glass-walled Gravity Bar with views over the city. Phoenix Park, a few minutes further west by bus, is one of the largest enclosed city parks in Europe, with a wild deer herd roaming freely.
For Georgian Dublin, the squares south of the centre — Merrion Square and Fitzwilliam Square — are among the finest streets of 18th-century architecture in Europe. Merrion Square also has the National Gallery and the Oscar Wilde statue.
Literary pilgrims have their own circuit: the James Joyce Centre, Sweny's Pharmacy, Davy Byrne's pub, and the Joyce Tower at Sandycove (30 minutes on the DART).
The Temple Bar district is tourist-heavy but worth a visit for the food market on Meeting House Square (Saturdays), the Irish Film Institute, and the traditional music sessions in its better pubs.