Seeking itinerary feedback

Greetings! Your trip depends on the type of things you enjoy doing, as you will see on the forum everyone has a different idea on what is a great trip. Here is an example of my trip to help you get started with your planning. We had to have a car. We flew into Dublin and rented a car and immediately drove west to Cong. We wanted to do a "hawk walk" and there is a great one at the Ashford Castle in Cong, we had a blast. We spent a couple of days in Cong doing the walk and checking out the Quiet Man movie area. We then went to Doolin for three days for the Cliffs of Mohr, the Burren, Doolin Music House, and music, pubs, sheep dog exhibition in the Doolin area. We then drove south to Dingle, seeing the sights of the west coast along the way. We spent 4 days in Dingle for many sights, for the Skellig ring drive, a private architecture/nature tour around the ring, and all kind of cool music, pubs, and food in the Dingle area. We then drove to Kenmare for 3 days, you can see from the map we were doing a counter clockwise tour of southwest Ireland. We did a private tour of the Ring of Kerry, we drove the Beara Peninsula, and toured the Kenmare area. We then drove back up to the Dublin airport where we left our car and bussed down to Dublin for 3 days. We did some hiking in each location, saw great music , had good food, and met wonderful folks from rural Ireland. In hindsight I wish I had gone out to Aran Island overnight and had visited Galway but I would not have traded our highlights, I would have added days. We loved the private tour of the RofKerry, the Dingle Peninsula, and our own driving tour of Beara. If I had to cut anything I would put more time in out to the northwest and less time in Dublin.....just my preference. Hiring a private driver tour for a day and a half gave me, as our driver, a chance to get a break and look around and the guides were awesome. Good luck

Good advice, and a pretty good sample itinerary, provided by the previous poster.
You'll definitely need a car to do justice to the sort of trip you're proposing. We love the Connemara area - Galway, not so much. Our preference for a base in the area is Clifden - close to the very pretty Sky Road scenic drive, the Connemara Loop including Cong, the village of Cleggan from which you can catch the short ferry ride out to the island if Inishbofin, and not far from the ferry landing at Rossaveal for the ride out to Inishmore.
For a first trip to Ireland I wouldn't waste time on Moher. The cliffs are nice enough but the crowds can be pretty off-putting. That time might be better spent just driving down the coast to Kilkee - lots of beautiful seascapes (and photo ops) and there's a pretty little cliff walk at Kilkee itself that you'll have pretty much all to yourself while the other tourists are jostling for position for their selfies at Moher.
Personally, I think that four full days in Dingle is about two days too many ... for Dingle alone that is. A better option is to base yourselves somewhere in the vicinity of Castlemaine or Glenbeigh, from which you'd be centrally located for a pleasant day trip to Dingle as well as the northern part of the ROK, including the very pretty Skellig Ring. That way you'd be able to unpack once for 3 or 4 nights while you explore the area, rather than running yourselves ragged by changing bases every other night trying to "see everything". As you say, this is an exploratory first visit. You'll be back - Ireland does have that effect on people. Point being that you need to resist the urge to dash from one site to another, but rather slow down and enjoy the country at a more relaxed pace.
No matter how you choose to organize your trip it'll be great. I wouldn't agonize too much about trying to craft the perfect itinerary. Get a good guidebook (or 3), sort out a general plan that satisfies your particular interests as 1st time travelers, then go for it, being sure to build in plenty of slack time to just let the day take you where it will - that's the true magic of Ireland.