7 days to see Ireland

Your going to hear this a lot but here goes. Too much in too short a time. Given the cost of airfare and the 1-2 days of jetlag, I don't go to Europe for anything less than 2 weeks. No way would I stumble jet lagged off a flight and drive a rental car 1-2 hours on the left side on unfamiliar roads. Fyi, most European rental cars are stick shift. If you're going to see Dublin, start there first then rent a car.

On lodging, here are some info sources. The Rick Steves Ireland guidebook and the section here on the forum for hotel/restaurant reviews. Also The Blue Book of Ireland list suggestions. https://www.irelands-blue-book.ie. My in-laws used it and were very happy with their stays.

I’d think a lot of the B&B’s may be showing sold out because they have no idea what next summer is going to look like or even if it will be a good business decision to be open.

I echo the thought of please don’t drive after a transatlantic flight, especially on the other side of the road.

The Dublin airport isn’t a great place to stay unless you’re taking an early morning flight out.

You may have already done so, but I would go back through older posts with questions very similar to yours. It’s hard to give advice because there are so many choices and your question was a bit vague, but here are some thoughts.

Stop at Rock of Cashel on the way to Killarney.
Take a night and stay in Cobh after Kilkenny - or
Stay 2 nights in Killarney or Dingle and then 2 nights in your next location. (Or 2 nights in Cobh or Kinsale and 2 nights in Killarney or Dingle - and skip Kinvarra).
The area around Kinvarra is pretty but I am not sure why you would pick there for 1 night. Are you thinking about that as a base for the Cliffs of Moher? If so, stay 2 nights.
Bunratty Castle also has the same medieval dinner (you probably knew that) and isn’t as far north.
Yes, drop the car off at the airport and taxi into town and stay IN Dublin. It’s easy to get to and from the airport and a taxi is pretty cost efficient for 4 people, as long as you don’t have too much luggage.

In one of your previous posts you indicated that your intention was to spend the first night in Dublin. My advice would be to stick to that plan in order to get a good night's sleep before you start driving. Maybe even add an extra night upon arrival as has been suggested in order to give yourselves one full day to explore the city ... and to allow you extra time to shed what's going to be a murderous case of jetlag after flying from the west coast.
Alternatively, you could consider reversing the order of your loop drive to begin in Galway. You could then take the train from Dublin upon arrival and spend that first night in Galway town before collecting your car for the short trip down to Kinvarra, giving you a leisurely driving day to explore the area around the Cliffs, Doolin, and the Burren before checking in to your accommodation in plenty of time for your dinner at the castle.
It's then a relatively short and pleasant drive down to Dingle.
We usually base ourselves midway between Dingle and Killarney (the stretch between Castlemaine & Glenbeigh), which allows us to explore both the Dingle peninsula and the Ring of Kerry without having to relocate every other day. Might be a more relaxing alternative for you too.
If you didn't want to deal with the long drive back to Dublin you could drop the car in Killarney and train back from there.
One-way drop charges in Ireland are pretty minimal - only about 30 Euros as I recall.

Robert, as always, gives excellent advice. It looks like, from your other post, that you are hoping to fly to Dublin from Bergen, though, so maybe no jet lag by that point? I missed that first time through. Good details to add to your question in order to get the most accurate advice. Arriving with no jet lag, I think I would still put Dublin nights at the end of your trip.

Stay 2 nights in Kilkenny. Then head over to the Cliffs of Moher via the Rock of Cashel and stay in Doolin 2 nights. Take the coastal road up to Kinvarra and spend the night doing the castle dinner. Then on to Dublin. Driving all the way to Dingle will add hours to your trip each way that you could be spending more enjoyably. We visited all these places (except didn't do the castle dinner) back in May 2018. Have fun!

Sunday July 25 Fly into Dublin from Bergen, Norway, Drive to Kilkenny 1.5 hours

Monday July 26 drive to Kinsale stop by Rock of Cashel and Blarney Castle

Tuesday July 27 stay in Killarney

Wed July 28 stay in Dingle Ring of Kerry

Thursday July 29 drive to Cliffs of Moher s and drive to Kinvarra and go to Medieval Banquet at Dunguaire Castle s

Friday drive to Dublin airport drop off car

Friday July 30 and 31 stay in Dublin

Sat July 31 Trinity College, Book of Kells, Grafton Street, temple bar, H’Penny Bridge

August 1 fly home

Also looking for places to stay. Having trouble finding a reasonable place in Dublin

Are you asking whether the itinerary is doable? If so, I would say yes, it’s doable but pretty ambitious. You may literally be “stopping by” Rock of Cashel and Blarney Castle. But I’m a slow traveler that likes to wander. You may not be so easily distracted.

Having said that there are two additional things that you may or may not have considered in your planning. The first is that Ireland is not in the Schengen Zone so I believe you will need to go through immigration on your entry from Norway. Perhaps someone else can confirm my suspicion. The second thing to consider is drive times. The general rule of thumb is to add 25-30% to the times estimated by the driving apps. Unless on the dual carriage ways it is rare to be able to drive the posted speed limit in Ireland.

As for accommodations, Dublin is expensive. The Premier Inns and Maldron Hotels are generally less expensive as our the hotels on the north side of the river. In Kinsale I recommend the Old Presbytery B&B.

Edit: in Dublin you can stay on the north side of the river and still be within reasonable walking distance to Trinity College, Temple Bar, etc. You could use walking over the Ha’Penny Bridge as part of the commute.

Staying anywhere near central Dublin during that timeframe is going to be very expensive - especially with 4 adults.
The further away from Temple Bar you go the cheaper the rooms will generally become, but then the tradeoff will be having to take the DART (the local commuter train system) or a taxi back into the city center to explore the sights.
As Trotter mentions, the Premier Inns are a good economical choice, but even they will likely be expensive in the city. For info, there's one located out near the airport that's usually much cheaper than anything you'll find in the city, and they offer family rooms as well which might be big enough to accommodate the 4 of you. Might be worth checking it out: https://www.premierinn.com/gb/en/home.html. The prices might even be attractive enough to permit renting two seperate rooms during your stay.
A taxi from the hotel into the city will cost about 30 Euros and will take about a half hour.
Kinsale is beautiful but it's a congested mess at midday when all of the day trippers are in town. I'd suggest timing your arrival for after 4 PM or so to avoid the worst of the traffic. Time and interest permitting, consider walking along the pretty shoreline path down to Charles Fort, with a stop at the atmospheric Bulman's Pub in Summercove along the way.

In Dublin, in July 2018, I stayed at Anchor House a b&b/guesthouse north of the river that was more reasonably priced than other options and very well located for walking everywhere, also very close to a City Link airport bus stop. I believe they had 20+ rooms including family rooms. Unfortunately, their website seems to be down now so I don't know if they reopened.