It's completely free to wander the grounds of Dublin Castle (pictured), although you can expect to pay a nominal fee to join a guided tour inside (around 5 Euros).
While you're there, be sure to pay a visit to the free onsight museums and library.
Ireland's most prestigious university, a trip to Dublin wouldn't be complete without seeing the 16th-century architecture of Trinity College up-close.
It is completely free to wander the grounds of the campus, which are surrounded by perfectly-manicured gardens.
Visit a church
While the city's two main cathedrals charge an admission fee, it's free to look around many of Dublin's smaller churches. Whitefriar Street Church, said to be home to the bones of St Valentine, is particularly special.
Take a free walking tour
Operating on a strictly tips only basis, Sandeman's New Dublin walking tours are run by native Dubliners who know all of the best things to see in town. You can pre-book online or simply show up at the designated meeting point in Dublin's city centre 15 minutes before the tour is due to start.
If you like parks, Dublin is the city for you. In fact, it's said to have more green spaces per square mile than any other European city, with 30 public parks dotted around the city to be enjoyed, whatever the season.
Window shop at a market
Even if you don't want to make a purchase (however tempting it may be!) the indoor Loft Market is a wonderful way to spend a few hours, especially if you are a fan of all things vintage.
Similarly, Temple Bar Food Market is also a great place to while away a Saturday morning. You can even sample some of the free gastronomic delights on offer from local producers.
Walk around Howth
Howth, a quiet fishing community that is now a seaside suburb of Dublin, is a beautiful place, and one best discovered on foot. There's an excellent walking trail available, taking you past a lighthouse, a castle and spectacularly-rugged cliffs.