If it's financially feasible I'd go to the southwest for a few days to see things like the ROK, the Skellig Ring and Dingle. Or near Galway in Connemarra which is also gorgeous..........and not worry about double paying for a few nights - it's worth it if you can. It would be pretty rough if you had three weeks in Ireland and were limited to Dublin.
If you are limited to Dublin there are fantastic day trips in the surrounding area. To echo the always accurate Diveloonie to the south are the stunning Wicklow Mountains and the monastic settlement at Glendalough. This is one of Ireland's most magical spots. Pick a nice weekday to go - avoid the weekend day trippers from Dublin. Remember driving time estimates are notoriously off in Ireland.... add 30% for driving times then factor in stops for food, gas etc.
To the north of Dublin the 5,000 year old toombs at Newgrange are incredible. The Boyne Valley and nearby Tara are wonderful as well. Also a quick trip to Belfast is nice too....and if it holds interest the Titanic museum is well worth a visit.
Another thing we loved as much as any of the "must see" sights was taking a leisurely drive out into the Midlands not really targeting anything, just roaming, discovering seeing totally non tourist Ireland and taking the time to interact with the locals. We are not outgoing folks but the Irish people welcome you in a way that is actually shockingly warm.....without even trying we've ended up getting invited to a home for dinner, or great fun conversations and getting tips for really special local, non guide book stuff. If you can just wander, stop and explore - it's fantastic.
Try and take some days in the SW if you can. If you can't .......enjoy the east.....it has a lot to offer. Dublin has some nice stuff but is near the bottom of places in Ireland for us but the great thing about Ireland is there is a magic almost everywhere if you take the time to look. Just point yourself in any direction, get out of the city and it will be wonderful.
Have a great trip !