Dublin the end of August, 2022

The Book of Kells exhibit is at Trinity College, very close to the Temple Bar area. After you see the Book of Kells, be sure to see the Long Library also. Quite spectacular. Also highly recommend the Chester Beatty Library. The Aircoach bus is a really good way to get from the airport to town and back.

Don’t waste your time sitting on the hop-on hop-off bus tour because you’ll be sitting in traffic all day. The best of Dublin is within walking distance where you are staying. Buy Rick Steves Snapshot Dublin guide (6th edition) and take the O’Connell Street Stroll self-guided walk.
I would also visit the visitor center (Rick Steves guidebook will tell you where it is) and sign up for day tours to Brú na Bóinne and Trim.

I would also recommend going out to Brú na Bóinne. Newgrange Tours by Mary Gibbons was excellent if you like history. Bus picked us and returned us to downtown Dublin (several locations). Awesome day tour.

Since you only have a couple of days, I wouldn't necessarily take a day trip (or even a half-day trip) outside the city. To get oriented to many of the places of interest in Dublin, I recommend the walking tour that begins at Trinity College. When we took it in 2016, it was supposed to be 90 minutes, if I remember correctly, but it stretched out much longer. We had to peel off from the group after about 2 1/2 hours because of another commitment. The guide was full of interesting information -- just a little more information that would fit into the advertised time frame.

Explore bus and taxi options for best airport connections. We've used both.

As was mentioned, the Airlink bus is the cheapest way to get into the city center from the airport. Can google their website to see if one of their stops in convenient to your hotel.
We generally rely on a taxi for the convenience involved, especially when encumbered with luggage. Costs a little more (about 30 Euro for the taxi versus 7 apiece for the bus) but we feel it's worth it for the door to door service.
Whether the HOHO bus is worth it will depend on just how far afield you want to roam. It does provide a good overview of the highlights of the city, including stops at some of the more distant places of interest like Phoenix Park and the Guinness Storehouse. Will save a bit of wear on your legs I think, and the live commentary from the driver is usually quite good for giving you a crash course on a little Irish history.

If your main interest is the area within Dublin city center then it's all easily walkable from the Temple Bar area.
You can pretty much satisfy your curiosity about Dublin in a couple of days, so booking a tour out to Newgrange and the Boyne Valley, or alternatively down to Glendalough and Powerscourt, would be well worth your time.

FYI there is no more Airlink bus to and from Dublin Airport. The new operator is called Dublin Express. It's mostly the same but of course check the schedule for frequency and exact stops. Air Coach is still operating as well though not nearly as frequent as before the pandemic; hopefully when tourism gets back to normal levels.

https://www.dublinairport.com/to-from-the-airport/by-bus/dublin-buses

I found the sights in Dublin very walkable except Kilmainham Gaol and Guinness. Walking in the city center and a taxi to the Gaol then Guinness (if of interest) and back to the city center would probably be cheaper and easier than the hop on/hop off. Try to spend some time, or at least walk through, St. Stephen’s Green.

For the Gaol be sure to get tickets. It to us was highlight of Dublin. Have been there several times and it is always interesting.

Merrion Square Park has an Oscar Wilde Memorial.

During my first trip to Dublin I used the HOHO bus. I saw that a lot of time was spent in traffic. But I thoroughly enjoyed the introduction. With subsequent trips to Dublin I’ve felt very comfortable walking, using public transportation, and a very rare but occasional taxi. As others have mentioned most sites are easily and quickly walkable.

Just piling on some of the above excellent tips:

The Gaol for sure.
We didn't do Book/Kells, but enjoyed the student-conducted tour of the Trinity College campus; free as I recall.
On our first day in Dublin we rode, and enjoyed, the HOHO bus; a relaxing get-acquainted overview.
Mary Gibbons bus tour to Newgrange; terrific.
Best meal: Matt the Thresher (specialty: seafood), near St. Stephen's Green if you're in the neighborhood at the right time. (Easy advance, on-line reservations available.)
Airport transit: in the interest of convenience upon our jet-lagged arrival, we took a cab into Dublin from the airport. Used the very reliable Airlink for the return trip.