As other posters said, don't spend much time in Dublin itself, it's really not on a par with any other European capital. Still, there's a few things to do there, or as a starting point:

In town:

• Grafton street and the area around, like Powerscourt Townhouse, George street Arcade market, Andrews lane Irish farmers market, grab a snack at the Irish Film Institute and see what they have programmed, Trinity College library, Temple Bar, Halfpenny bridge, O'Connell Bridge, O'Connell street, Moore street's market (my favorite). Visit the Guinness brewery and the Jameson distillery, have a tea and some pastry at a Bewley's Cafe, a fish and chips in some cheap place.
• Pubs: Pub crawl in Temple Bar and south of O'Connell Bridge, have an Oyster Stout at the Porterhouse (also one in Bray on the sea front where I lived), listen to music at the Cobblestone. Try the pub food in different places, it's usually great. Here's some more:
  • Mullligans, Poolbeg Street (some say the best Guinness in Dublin)
  • Kehoe’s, South Anne Street (get there before the suits arrive at 5.30pm)
  • Neary’s, Chathnam Steeet (for civilized conversation)
  • Grogan’s, South William Street (perfect Saturday afternoon spot)
  • The International, Wicklow Street (an institution)
  • The Long Haul, South Great George’s Street
  • The Upstairs Lounge in the Central Hotel (comfy, cozy)
  • Sackville Lounge, Sackville St, off O’Connell Street (the real McCoy)
  • The Palace Bar, Fleet Street, Temple Bar (a gem)
  • The Stag’s Head, Dame Court

Out of town:

• Take the DART (Dublin rail transit) south to Bray, take the seaside walk between Bray and Greystones, grab a lunch at the pub and walk back or take the double decker bus back to Bray then the DART back to Dublin (you took a return ticket, right?) There are some guillemots penguins along the seaside walk, and it's magnificent. About 30 minutes walk one way.
• Take the DART north to Howth, walk north to Howth Head, make the full 2 hour loop to Sutton and take the DART back.
• Wicklow: Drive to Powerscourt estate, visit the castle and gardens, go to the waterfalls where young Merlin retrieved the sword (in the movie). You can push to Glendalough and Gap of Wicklow.

One week is not much, I would spend most of it in Kerry (Killarney, Gap of Dunloe), Doolin, Cliffs of Moher, the Burren. You don't drive very fast on Irish roads. Typical cars would Ford Fiesta size. Try selecting a European brand like the Opel Corsa.