We'll be in Ireland for a very short trip in the end of May 2014. Including the day we fly in, we'll have 6 days. So what should our sightseeing priorities be? We'll have 4 adults and 3 teenage boys. We don't mind renting a vehicle and driving. Thanks for any suggestions.
So you really have four days (don't count your departure day, since it won't be usable for sightseeing). Car would be the best way to get around except for any time you plan to spend in Dublin. Best would be if you fly into Shannon and out of Dublin - avoids backtracking. Landing in Shannon, you could see the Cliffs of Moher, then you could drive down to Killarney. I would try to fit in Blarney (more there than just the castle), the Rock of Cashel, Glendalough, and Dublin (Kilmainham Gaol, hop-on hop-off bus tour, Grafton St, Trinity College). Www.viamichelin.com is a good resource for planning routes, looking at distances and driving times (add 25% to their times - driving can be slow in Ireland).
With 7 full sized people you will need a van large enough for passengers and luggage or 2 cars. If you plan to spend time in Dublin you won't need or want a car there. Where will you fly in and out of? What interests you? It's hard to tell people what their priorities should be without that information.
You may be too big of a group to rent a car, and back roads in Ireland are tight and can be frightening for a first time driver in Ireland, even for those who rent tiny cars. A mini van would be a different story! If you are brave, go for it, because then your schedule is much more free. Public transportation in Ireland covers the bases but leaves much to be desired (I am an American living in Ireland right now and only rely on public transportation. It gets me around, but it has also left me stranded!).
If you are renting a car, spend the first two nights in Dublin. Then drive directly to Galway for a day and night. From Galway, drive down to Dingle, touring the Burren and Cliffs of Moher en route. If you have the time, take the road along the Shannon Estuary after you leave Limerick rather than the direct highway to Tralee, because the coastal road takes you past a ton of ruins, which were originally points that collected tariffs as people rode their boats down the estuary. Stay in Dingle for two nights. On your full day in Dingle, tour the peninsula. If you are the energetic types, rent a bike for your tour! I did this in gale force winds and sleeting rain, and it was still one of the best experiences I've had in Ireland. I tell my friends who visit to do that, too, and they absolutely love it. If you aren't for the 30 mile cycle, take your car around the peninsula. My family did that and they also very much enjoyed their experience. If you are flying out of Dublin, it's about a 5-6 hour drive from Dingle to Dublin. If you are there for 6 nights, you can sleep a night in Cork or Limerick to break up the travel time a bit and not be so rushed the day you fly out (unless you are flying out of Shannon, then definitely stay in Limerick). If you only have five nights of sleeping, consider reversing your trip - start in Dublin, then go directly to Dingle, up to Galway (with the Cliffs and Burren en route), and then back to Dublin to fly, since the drive from Galway to Dublin is only 2.5 hours.
Hope this helps!