If you are arriving early, we did the tour out to Newgrange (with Mary something or other,lol....on my phone) which was excellent. We also enjoyed the National Museum as I particularly wanted to see the Bog People. I also really liked the Chester Beatty (museum and library). Not only was the collection interesting but it was actually well-airconditioned which might be something to keep in mind in July, lol!
I was disappointed in my experience at the Book of Kells. It was jammed around the book and you literally had to elbow your way to the front. This was a number of years ago so hopefully they've changed the system (or actually "added" a system, lol) and are restricting the number of entries so it is easier to see
Because of this, to me there seemed to be plenty of time for both the Book of Kells and Kilmainham Gaol.
editing to add: @Simpgolf - yes! to seeing Iona on the Best of Scotland tour. That was very cool to complete that connection.