Generally I recommend getting your car at the airport so you can hop on the M50 and avoid driving in downtown Dublin. In some cases it would make sense to pick it up in a city location. It will depend on time of day, day of week, location, etc. You will need to find out what locations your car rental company has available.
I agonized about picking up a car in Dublin city centre or at the airport, because the airport location opens so much earlier in the morning. Then I realized that since my drop-off time at Shannon was in the afternoon, I could actually pick up the car in the afternoon prior to our departure and not pay for an additional day. I see from your other post that you are staying at JurysInn Christchurch, which is exactly where I stayed. There is a car park (separate management but attached to the hotel with a direct access) right behind the hotel. I personally found it very convenient to set off on our journey into the country with the car just sitting there, ready to go next to the hotel. We got on the road early on a Wednesday morning and probably avoided a lot of traffic because we pulled ourselves together good and early, but I really felt it was worth it. We didn't spend a whole morning just getting the car; it was already there!
We got the car from Dan Dooley, which I found very good. Their city location is behind Trinity College. Just know they close for lunch from 1-2.
By the way, there's a nice breakfast spot around the corner from JurysInn Christchurch. Good food and less expensive than the hotels. Go out the front door to the right, make the first right and go down the hill a short way. You will see Applewoods Cafe.
I'm glad that worked out well for you to get your car a day early. And no extra charges are always good! Thanks for your advice. It may well work out to IrishEyes' advantage to do the same. It all really depends on individual circumstances. Thanks for you input.