We're thinking of booking an independent "tour," but they get you from Point A to Point B, which seems a whole lot easier than driving ourselves or navigating ourselves. Any experiences?

Driving in Ireland isn't bad, truly. Just don't drive a long way when you're jet lagged, keep reminding yourself to stay on the left (became natural for me after one day), and keep in mind that you WILL get lost at least once and that getting lost is fun. Driving allows you to do and see what YOU want rather than sitting on a bus all day; you can stop and take pictures, take a detour, stop for lunch wherever and whenever you like.

Don't drive in Dublin, though. No need. And if driving will stress you out so much that you can't look forward to your trip, well, by all means take a tour. But otherwise, rent the smallest car you can and enjoy.

Second jent's suggestions!

The problem with an organised tour is they go from A to B to C - but what if you want to stay an extra day in B - or explore that peninsula/castle/village/pub a bit longer?
Driving in Ireland is easy and delightful. AS the others have said it gives you the freedom to see and explore what you want to see and explore, not what some tour guide thinks you should see and be lectured about.
Just make sure you stay either in the local pub or within walking distance of it if you hire your own car .

I don't drive in Ireland. Most Car rental Agencies have an age limit (75) and I'm 78 now. But I get along fine on Bus Eireann http://www.buseireann.ie or CityLink http://www.citylink.ie
Citylink has a Bus Service that departs Dublin airport hourly and takes you to Galway in about 4 hours. It's good for me for getting over jetlag and arriving at my Galway B&B (or Hotel) at a reasonable time for check-in.

You mention Tenon and CIE Tours: Have you researched Paddywagon tours http://www.paddywagontours.ie they have some great itinerarys

Take a look at www.irelandexpert.com (Note the 5% discount if you book a CIE tour through Pat.)

You'll find tons of information on planning an independent trip. I had originally decided we'd rent a car, stay for several days in three or four places, and take day trips with tour companies (thereby not having to do all the driving).

But, one of Pat's tours included everything we had in mind, so we booked that. Right away, we were quite relieved to be able to sit back in a comfortable coach and enjoy all the scenery all along the way everywhere without worrying about any driving at all.