Free Walking Tours
Sandemanns Walking Tours - I thought this was good, it encompassed most of the important information on the city and country as a whole, but it didn't go near O'Connell St which was disappointing.
O'Connell St and the Spire
The real stars of O'Connell St are the GPO (General Post Office) and the statues - many of which still have bullet holes from the 1916 Easter Rising almost 100 years ago (the Rising was the first in many events which eventually led to Irish independence from the British). The Spire is a new addition and a new popular landmark and symbol for Dublin - although it's not much to see, just a really big needle!
Phoenix Park
This is like the biggest metropolitan park in Europe or the world or something, but all you need to know is that it has wild deer and if you're around early in the morning you could spot one (or several)! It's also home to some other places like Dublin Zoo (good but a little expensive I think) and the residence of the President (free - see below).
Aras An Uachtarain (The official residence of the President of Ireland)
This has tours every hour from like 10am to 3pm every Saturday only. It's free, but you should be early to ensure you get a ticket.
Ha'Penny Bridge
This is one of the locations from the book Ulysses by James Joyce, and a short walk from O'Connell St in the city centre.
Ha'Penny Bridge
Leinster House (home of the Irish Parliament)
I haven't got around to this yet, but apparently there are a few tours a day Monday to Friday, but places are limited.
National Gallery of Ireland
I once overheard an American tourist refer to this as "the art centre" which was incredibly offensive. I have zero interest in art, but from what I understand there are some important pieces on display here, and it has a central location too.
Archaeology Museum
There are three national museums in Dublin (the other two being natural history and fine arts) but this one is the best, and definitely worth a visit. It boasts a big collection of Celtic and viking items, as well as a few famous pieces like the Tara Brooch, Ardagh Chalice and a few 'bog bodies' - bodies preserved for thousands of years in Irish marshland.
Natural History
This is a really old, musty museum full of dead and stuffed animals. Definitely quirky, but quite small and not worth a visit if you only have a limited time.
Fine Arts
Located in an old military barracks. I haven't had time to visit yet, will update when I do!
Chester Beatty Library
This has the worlds largest collection of Kor'ans. Or something like that? I really liked this place, it's modern and the collection is a cool mix of things from around the world.
Trinity College
This place really isn't that special these days - any Irish student can choose to go there if they wish, it's not fee paying, prestigious or only open to really smart people. But it is home to the Book of Kells (it usually costs money to go in - but grab a passing Trinity student as they have free entry and can also bring a guest for free!).
Temple Bar
Temple BarThere really isn't much to see here, I've heard it being compared to some of the 'old towns' around Europe, but it's definitely not on par with any of these! It's popular for having cobblestoned streets and lots of bars which are incredibly overpriced and popular with tourists.
The Science Gallery
This has exhibits which change every few months, it's interesting but small and again not worth a visit if you have limited time
Irish Museum of Modern Art
I may have already mentioned my indifference towards art, and therefore I haven't made it a priority to visit here yet, so cannot comment on anything except the fact it's free ;)
Docklands
Dublin Docklands
This area was falling apart for many years, but has undergone complete redevelopment and is now home to hundreds of shiny new offices housing international companies like Google and Facebook. The area also boasts the Convention Centre, 3 Arena, and lots of new bridges. If the weathers nice and you have some free time, it would be nice for a stroll.
The main places for shopping in South Dublin city are Grafton Street and the adjoining Stephens Green Shopping Centre, while north of the river you should visit Henry Street and the adjoining Ilac and Jervis Shopping Centres.
If you're a fan of Primark/Pennys, you'll find one of the biggest ones in the country on Henry Street, a 5min walk from the Spire on O'Connell St. You'll find Europe's first Forever 21 at Jervis Centre, and the Disney Store is on Grafton St. The main tourist gift store is Carrolls, which have a few locations around the city. Obviously it's overpriced, so maybe check out some of the smaller shops too.
