The city of Dublin is filled with places to explore.  You may wish to give yourself an overview of the city by taking one of the Dublin Bus hop-on-and-off tours that will take you to all the main landmarks.  It is an open air bus, so you will have perfect views of all the sights, major and minor.  Among the many highlights are the homes where the Duke of Wellington and Oscar Wilde were born, as well as the beautiful Christ Church Cathedral, St. Patrick's Cathedral, the Molly Malone statue and  Dublin Castle .
The bus will also get you to the outlying attractions such as the Guinness Storehouse, which you won't want to miss.  You may want to have lunch in their restaurant with its good views of the city.  The tour is worth your time.  Taste the hops and see the displays, all very well done and then end up in the Gravity Bar, perched on the top of the Storehouse.   Its sweeping views are the best to be had Dublin . 
If you are staying in the city centre, you can stroll to TRINITY College 's wonderfully quiet quadrangle, and after being impressed by that scene, make your way to the exhibit about the Book of Kells and other manuscripts.  Be wary, you may find some enterprising students offering you an added-price guided tour as "the only way" to see the Book of Kells.  Nonsense!  There is a standard admission through the gifts shop.  Take your time when you tour, there is a lot to see -- ancient artifacts having to do with writing in general and Christianity in Ireland in particular, including displays of ancient jewelry.  In the Book of Kells room normally only two pages are displayed and the lighting is dim, so wait your turn and then linger and enjoy admiring this ancient treasure.  Then your tour goes upstairs to the impressive Long Gallery and do make your way to the far end where the other copies of the Book of Kells are on display, without much fanfare          

For those inclined to do some shopping with sight seeing turn left outside TRINITY College and stroll up Grafton Street as far as the St. Stephen's Green Shopping Centre --a modern day glassed-in mall with many shopping choices  or turn right  outside TRINITY College and  stroll over O'Connell Bridge along O’Connell Street    see the G.P.O and the Spire, (at night   lighted to resemble an upside down exclamation point)  then left down Henry St. more shopping opportunities and left again onto Liffey St. then over the Ha'penney Bridge, (a symbol of Dublin) cross the road on the far side of the bridge , walk through the archway into  the Temple Bar area.

 

There are many good places to eat locally but for atmosphere and traditional boxty try Gallagher's Boxty House in Temple Bar   For a fascinating interior  (an old Victorian bank) and delicious food try The Bank  20-22 College Green for steak pot pie or mushroom and ricotta strudel, a pint or a coffee or  O'Neill's at the end of Suffolk St. close to the Dublin Tourist Office. This is a beautiful Victorian pub, the interior has a series of interconnecting rooms, they do a great carvery lunch, as well as an la carte menu and have an excellent reputation