The National Museum on Kildare Street, Natural History Museum on Merrion Square and National Art Gallery on Nassau Street are all free entry and really interesting. Some exhibitions in the gallery have a fee but main gallery open access.
Some ready interesting history.
There are mummified tombs in the crypt of a church to visit.
Bram Stoker lived there, and thee is a ghost bus tour at night of various spooky type things.
St Patrick’s Cathedral is interesting too.
Trinity College and the Book of Kells.
And Glasnevin Cemetary.
Get the DART out to Dun Laoghaire, Howth it Bray. All have lovely walks along seafront. Howth great seafood. Dun Laoghaire the largest harbour in Europe and can walk around it along both East and west Piers ((there’s an old naval battery and soldiers quarters at the end of the East Pier, and Teddy’s ice cream now have an outlet there, Teddy’s is a DL institution!)
All sorts of bus tours - including the Splash Tour which has quirky guides doing a potted history of Dublin and has a trip on the water around Grand Canal Basin as part of it (amphibious vehicles from WW2).
Lovely parks in city Centre - St Stephen’s Green and Merrion Square in particular. Ducks in the pond are greedy on the Green, Sunday morning artists set up around Merrion Square and some good paintings on offer.
And walking along the canals is lovely too.
A mix and high street and more quirky shopping.
Great food in any style you want, and from artisan food markets up to michaelin stars.