Hello -- I'm planning to fly into Shannon, pick up a rental car -- explore Dingle / Doolin for 5 days, then head back to Dublin to then spend 2 days exploring. To avoid Dublin traffic, etc, I've arranged to drop the car off in Limerick (heading there from the Doolin area) and catch a train to Dublin. I'll be staying downtown Dublin in the Temple Bar area. Any alternative suggestions for where to drop the car off and/or sites to see along the way if I drive from Doolin to Dublin? (I know there are some & I won't see everything. It's a long enough travel day to get from Doolin to Dublin.)
The place that immediately springs to mind for me is Birr Castle. The builder was a leading astronomer in the 1800s (largest scope on earth for awhile) and the castle and gardens are pleasant. The garden has a accurate scale model of the solar system. The science museum on the 2nd floor is impressive. The telescope is cool, of course. If you don't want to divert that far off the direct route, I'd suggest Athlone (Castle). There are lots of things to see along the way. Your drop-off fee may increase by using Dublin (fairly unpredictable how their algorithms work).
Talking as someone that loves Irish music (sessions, in particular), I can't exaggerate how much I dislike the Temple Bar area. Hopefully your lodging isn't close by, or you'll never get any sleep. There are some hidden gems in the outskirts of the zone, but good luck!
The only placce I would add to jjgurley's excellent suggestions of Birr and Athlone is the early Christian site of Clonmacnoise with its ruined churches and cathedral, round towers and carved crosses. It is a lovely site on the banks of the River Shannoon.
If you have the option to reschedule your car return location, and if your rental company has an office there, Ennis is closer than Limerick to Doolin. The way the tracks are laid out, it’s a shorter train ride to Dublin from Limerick, but first you’d have to get there.
Alternatively, turn your car back in at the Shannon airport where you got it, then take the bus to Ennis, and the train from there to Dublin.
Or, if turning in the car at Shannon, another option is go from there by train to Limerick and then transfer there to the train for Dublin.
For the majority of the day the train from Limerick to Dublin is a change at Limerick junction, into a train from Cork.
In the afternoon there is also one train which takes the little known or travelled back route towards Dublin, and is instead a change at Ballybrophy (from memory).