Help me figure out bases around Ireland for sightseeing.

This is the strategy we have used to plan about ten European road trips. So far, it has worked well for us. (Sorry about the weird formatting - it looks correct on the preview page but not on the viewers page.)

1. Choose region (not country) you want to visit. Example: northeast corner of England would include the borders area
   of Scotland. If you are visiting for multiple weeks, you could do one region per week, depending on how in depth
   you want to go. Do you want an overview of several areas or immersion in one area? Both work well,
   depending on your preferences.

2. Order two or three guide books. Rick Steves is good, but he skips lots of areas based on his personal choices. I also like
   Lonely Planet and Rough Guide. Michelin green books have lots of information, but are not conveniently organized.
   Carogan guides are my current favorites. Read / skim guide books, concentrating on what you want to see.
   Don't worry yet about hotels and restaurants. Highlight as you go!

3. Order a map of the area. Michelin ones are good. Highlight the places you want to see.

4. Look for a town which is in the center of several of your chosen sites. Depending on how many sites there are, stay in the town
   two to four nights. We like small towns (Clifden, Kenmare, etc.) for lodging. Plenty of walkable choices for dinners, yet easy to
   get out of them for sightseeing. If you are visiting two or more regions, you might need a one night stand as you transition to
   the next region. Plan two or three interesting stops for those travel days.

5. For your actual trip, get a road atlas or use GPS if you like them. Others seem to prefer the spiral bound, but I like the larger
   format atlas with the staples. Spiral pages seem to tear out too easily. Highlight your route as you travel.

Don't hestitate to spend some of your travel budget before you go on some good travel guides and maps. These purchases are a small part of your overall trip expenses and are an essential and enjoyable part of your trip planning. When you travel, take only the relevant chapters of your travel guides.

Hope this helps.

Thank you for the info Cynthia

All good advice from Cynthia. My two cents:
We, too, like to find a central place to stay for 4-7 nights and day trip around an area from there. Our preference is to find a place close to, but not in, one of the cities so we can visit it during the day but then leave the hustle and bustle (and the crowds) behind when we return home in the evening.
If Dublin is a given for 3 or 4 nights I'd suggest exploring the city on foot, or via the HoHo bus, and taking advantage of some of the very good day trips offered to places outside the city ... Newgrange, Tara, the Boyne Valley, etc. you'd neither need nor would you want the hassle of a car in Dublin - it's just more of a pain than it's worth.
Suggest getting your car on the way out of Dublin (the airport has a wider selection of cars, with more likelihood of getting an automatic which we highly recommend). Arriving at any of the popular tourist sites in the early morning is a good strategy to beat the crowds, never more so than at Glendalough. Although the visitor center doesn't open until 9:30, the monastic site itself is always open, so if you're there early you'll pretty much have the place all to yourselves.
Rather than staying right in Waterford I'd suggest the pretty village of New Ross about 30 minutes away. It's a much more mellow place with a nice small town atmosphere, and is also handy to the Hook peninsula, the JFK ancestral homestead, and some very pretty countryside along the River Barrow.
Kinsale is a great choice. Day trips to Cobh, Cork and the walk down the river to Charles Fort are very pleasant outings. Stop for a pint or a pub lunch at Bulman's pub in the hamlet of Summercove - you walk right past it on the walk to the fort. Fair warning though - once you're in there you probably won't want to leave.
Many here recommend Kenmare over Killarney, which has gotten pretty congested in recent years. Kenmare is handy for exploring the National Park and the south and west side of the ROK, including the exquisite Skellig Ring Road out to the village of Portmagee where you can visit the Skellig center and (weather permitting) book a boat trip out to Skellig Michael. Kenmare is also handy for exploring the Beara peninsula just to the south - which we consider one of the best kept secrets in Ireland.
Rather than staying in Galway town I'd suggest the pretty little village of Clifden about an hour further west. It's central for exploring the Connemara Loop and is only about 45 mins to the ferry landing at Rossaveale for day trips out to Inishmore. Another treat is a daytrip out to the island of Inishbofin, which departs from the town of Cleggan. The Sky Road west of Clifden is one of Ireland's great scenic drives. An interesting (and haunting) excursion would be to drive out to the Doolough Memorial. Can google it to learn about what happened there and see if it might be of interest.
One publication that we always bring with us is "Back Roads Ireland" by DK publishing, which contains lots of off-the-beaten path excursions that you won't find in other guidebooks. Can find used copies on Amazon for just a few dollars. It really is a terrific resource.

Robert, thank you so much for all this info. I’m off to research all your suggestions. Thank you thank you thank you.