Staying outside of Dublin - Looking for Day Trips and Donegal Advice

For Dublin proper I would definitely book tickets for Kilmainham Gaol and 14 Henrietta Street. The former you've probably read about. The latter is a Georgian townhouse that has been "remodeled" to mirror the ups and downs of Dublin. https://14henriettastreet.ie Other historical sites include the GPO and Dublin Castle.

Day trips that I personally consider as "must sees" are the Rock of Cashel, Glendalough and Newgrange/Bru na Boinne. A visit to Bru na Boinne could include a stop in Trim and Trim Castle as well. The Trim Castle tour is interesting because it includes the history of how the castle was transformed over the years. Be aware that Trim Castle is a defensive castle, not a stately manor house (no silver tea services and tapestries).

Slane Castle is north of Dublin. You can tour both the house and the distillery, which is located in the former stables of the estate. You used to be able to dine in the castle, but it looks like you can only eat outside currently. Certainly worth a few hours if you are in the area.

If you still have some flexibility built in to your plans I'd suggest modifying your itinerary a bit to make better use of your time.
Here goes: upon arrival at Dublin airport catch the express bus to Galway. Once there you can spend a night or two, then pick up a rental car to explore Connemara - our favorite part of Ireland. It's a Gaeltacht region, meaning that you'll hear a lot more of the Irish language spoken than in other areas of the Republic. The road signage will be in Gaelic too (though with English subtitles). There's very pretty loop drive from Galway heading NW to the market town of Clifden (where we usually stay) which is the starting point for the beautiful Sky Road scenic drive - one of Ireland's best. Continuing the loop around you can visit Connemara National Park - a great place for an easy hike up atop Diamond Hill for panoramic views of the countryside all the way to the sea. There's a nice coffee shop there too. Further on are Kylemore Abbey and the village of Cong. Asheford Castle there is a favorite here for the Hawk Walk they offer, plus the village still looks like the movie set it was back in the 50's when the old John Wayne/Maureen O'hara flick "The Quiet Man" was filmed there.
You'll pass a few peat bogs along the way, with some of the locals out harvesting the stuff the same way they've been doing it for hundreds of years.
A short detour to the north will take you to the Doolough Valley and memorial, which we've always thought was one of the most evocative places in Ireland because of the history of what took place there. If you're truly interested in Ireland's sad history then I'd rate Doolough as a must see.
You could spend several more days in the area visiting the Aran Islands or Inishbofin, or you could continue north into a bit of Donegal - Ireland's Wild West which will indeed take you well off the usual tourist track. Returning your car in Galway or driving back to Dublin and returning it there for your last 2 or 3 nights would allow you to stay in your Air BnB and still visit the city and the Boyne Valley as others have suggested.
Doing something like this might streamline your itinerary a bit.

Thank you for the input - especially the suggested itinerary - we will be mapping out our trip this weekend so this is very helpful. Our original plan was to just do day trips from our AirBnB, but then my mom kept exploring websites and now wants to be more adventuresome than first planned :-) I hope our hosts don't get mad if we cancel or shorten our stay.

If you only have 1 week, I would pick 2 places max to see. I cant imagine driving to Donegal from Dublin for a day would be very enjoyable. Even a one night stay seems like a waste of time. I would say Galway and Dublin (since you already have a place there). See the things within an hour or so of your accommodations. You dont want to spend the day driving and not actually experiencing Ireland.

Agree with khalloc. Lots to see in Donegal but more time needed. Based on my experience driving on 3 separate trips to Ireland I would add that you're well advised to allow 33-50% more driving time than your Google maps indicate, especially if you will be covering many miles on the secondary roads.

The monastic site at Glendalough is indeed a highlight, but there's another terrific monastic site at Clonmacnoise which is much less crowded. It's located on the banks of the Shannon and is an easy enroute stop if you elect to drive back to Dublin from the Connemara area.
BTW, the one-way drop charge for picking up a rental car in Galway and dropping it off in Dublin is pretty minimal.

Robert has proposed a great itinerary, most of which we did over a four day period in Connemara. I'll add a couple more items to consider.

1. On the day we did the Sky Drive and Doo Lough Valley, we also visited Killary Sheep Farm on the Killary Fjord. Sheep dog demonstration, sheep shearing and feeding lambs alongside the fjord which is beautiful. At one end of the fjord is the village of Leenaune with several good lunch options and a small but interesting sheep and wool museum.
2. The island of Inishbofin was delightful. A short ferry ride from Cleggan, you can spend a wonderful day there.
3. Croagh Patrick and the National Famine Memorial in County Mayo are also easily accessible and worth seeing IMO. Also in County Mayo is the town of Westport which was highly recommended to us although we didn't make it there.
4. Going south from County Galway into County Clare you can easily see the Burren and Cliffs of Mohr in a day.

We spent a week in County Donegal and while we loved it, I would not recommend going for a day. You won't get a good feel for this beautiful remote area of the county in day trip and it's a lot of driving.

Whatever you do it will be wonderful. Ireland may be my favorite of all the trips I've taken.

I agree with Trotter about going to Trim and Brú na Bóinne that’s located north of Dublin.

Another vote for Trim and its castle. If you want to travel south and be with nature, visit Glendalough and the Monastic City. There’s also a nice waterfall there. Avoca, also south, is a small town with a woolen mill on its outskirts if you wanted to visit one. There’s not much to the town, but it was the filming location of the UK tv series Ballykissangel..