This is probably blasphemy to many folks, but some would argue that Ireland's best attractions (and certainly its best scenery) is found away from the big cities. We did a trip just a little longer than yours, and we only spent one night in Dublin (our last night, since we had an early flight departing the next morning). The rest of our time we spent on the west coast and southwest of the country. We loved every bit of what we did and saw. We know we will return to Ireland for subsequent trips, and we will probably spend more time in Dublin (but also want to visit other parts of the country).
Although Dublin certainly has its charms, if you've got roughly a week, I think it would be a shame to spend all of it in Dublin or any city. As Chani suggested, upon arrival in Dublin, you might grab a bus to Galway, on Ireland's west coast (get the bus at the airport, easy and comfy), and press on to there rather than try and struggle with things when you're exhausted (most flights from North America arrive in the morning, this makes a good use of your first, jetlagged day). From Galway, there's plenty of good things to see and do for a few days. Then back to Dublin for as many days as you choose, and you're ready to catch your flight home.