Where to stay for 2 day layover in Dublin

The Temple Bar area near Trinity College is smack in the middle of things, but anything there will be quite expensive and pretty noisy in the evening as well - there are a lot of pubs in the immediate vicinity.
Prices will generally decrease as you go further away from the city center, so the tradeoff will be the time and cost involved in getting from your accommodation back into the city to sight see.
We've stayed here a couple of times and can recommend it https://www.theleesonlodge.com/. It's about a half mile level walk to Temple Bar and there's a bus stop for the airport shuttle (about 7 Euros) right in front of the place. They used to offer a pretty good breakfast too, but I don't know how Covid restrictions may have affected that.
We usually rely on booking.com to explore options whenever we travel to a new place. Their cancellation policy is pretty liberal, and we find the search engine to be quite handy for getting an apples-to-apples comparison of available options, pricing, and location.

Harding Hotel

Hotels north of the River Liffey will be less expensive than those near Trinity College and St. Stephen's Green. A number of posters have spoken highly of the Hilton Garden Inn - Customs House. There's also a Holiday Inn Express on O'Connell Street Upper. Both would still be within easy walking distance of Trinity College. I have not stayed at either. Further afield you could look in the Ballsbridge neighborhood which is a 2-3 kilometer walk but on the Dart light rail system. There are B&B's in Ballsbridge.

Stayed at the Harding Hotel twice. Once we stayed above the pub and the music and noise kept us awake at least half the night. The other time we did not stay above the pub and didn't have a noise problem at all. Just the luck of the draw. The accomodations, breakfast, and the rest of the hotel are fine.

I can recommend the Davenport, I"m so-so on the Jury's Inn Christ Church, and suggest you stay away from Buswell's.

I stayed at Hilton Garden Inn customs house. Pros: Nice hotel and we had a great view of the river. Directly on the express bus line to/from the airport and 1 block away from the tram. It was a 10-15 minute walk to the more popular tourist area.
Con: We didn't really have any, but some people may feel that riding a tram for 5 minutes or walking for 10-15 minutes is too inconvenient. It is a matter of personal preference.

We stayed at the Harcourt Hotel in Harcourt Street, an easy walk from St. Stephens Green, Grafton Street, and Trinity College. The airport bus stop is around the corner. Since you only have 2 days, I'd recommend paying a little more to be located near points of interest instead of having to spend time "commuting" to a hotel on the north -- less interesting -- side of the Liffey. Plus, you won't be paying for transit back and forth.

The Harcourt was clean and attractive, with helpful staff. We arrived on a redeye flight in late morning local time. Our room wasn't ready quite yet, but they welcomed us, offered to hold our luggage (we were happy just to cool our heels in their lounge) and got a room ready for us ASAP at no extra charge.

Drawback: there are several nightclubs on that block. It looks like a regular residential street, but come midnight it's a different world. The noise from 1 AM all the way through to daybreak was remarkable. We were there on a Fri & Sat night in mild, dry weather, so (inebriated) people were all out enjoying themselves. If you're there during the week, or in inclement weather, it surely won't be that bad.

We did a lot in our 48-hour stay, focusing on the activities and sights with the most stars in the RS guide, as well as those that personally interested us the most. Dublin is a lovely city!

Years ago we stayed at Albany house by St. Stephen’s Green. Close to all the sights but away from the crowds. The bus stop to the airport was right at the Green.