Ireland in 10 days

Have you already booked your flights? Presumably you haven't booked your lodging.

I'd recommend at least two nights in Dublin, maybe three. Lots to do there. You could also stay an extra night or two and do some day trips (Glendalough, Bru na Boinne, etc.). I would highly recommend spending some time in County Kerry, preferably in Dingle and the Dingle Peninsula, although others might stump for the Ring of Kerry. Kilkenny is a great medieval town, and the Rock of Cashel isn't far from there (well worth a visit). Not very familiar with Cork. We found Galway to be disappointing. I think the Cliffs of Moher are a must see if you are on the western side of the island.

Not sure if you are interested in Northern Ireland, but Belfast is a short train ride away. Others would no more about Northern Ireland than me.

What are you interested in seeing? Are you going to have a car? These are the two biggest questions you failed to give any guidance on in your post.

You need to get the RS Ireland book, of course. Dublin is a must and you need a minimum of two full days. I would recommend not counting your jet lagged arrival day as one of those. See the Kilmainham Gaol, Irish Archaeological Museum, Trinity College/Book of Kells, musical pub crawl (tour), Chester Beatty Library, Dublin Castle and enjoy walking some of the scenic areas of the town. If you want you can see Newgrange and other sites north of Dublin in a day trip out of Dublin but that would add an extra night in Dublin.

Key highlights in my opinion are Glendalough, Rock of Cashel, Dingle Peninsula and Cliffs of Moher. Add Galway if you can fit it in. Get the RS Ireland book and plan it down tight. You will have a busy 10 days if your goal is to see as much as practical.

Rick pushes Northern Ireland but I would personally skip it on a first, short trip. Going back and forth takes up too much time for what's there and the trouble it would add.

To the suggestions above, I would add the Burren, a unique and starkly beautiful limestone formation with interesting prehistoric sites. In the late spring the wildflowers are amazing.

Also, I suggest getting another guidebook in addition to the RS guide. The RS giudebook is pretty restrictive in the areas it covers. The Blue Guide is amazing for art, architecture, history, prehistoric sites. The DK guide is pretty comprehensive. And if you're going to have a car, the DK guide to scenic drive is really good.

To add to the other suggestions Galway was my favourite town out of all the places I stayed. There is so much to see and do from there, and it is not crazy busy like Dublin. The Connemarra region, the Burren, the Cliffs of Moher, and the Aran Islands can all be easily done from Galway, and each area would be a day trip. I would not miss a day trip to Newgrange from Dublin, it was definitely a highlight as the tour included other stops along the way. The Rock of Cashel is also a great place, but if you won't have a car it will be time-consuming to get to by train or bus. I certainly enjoyed the Killarney area, also, as the Gap of Dunloe and the Ring of Kerry or the Dingle peninsula can be day trips from here. Ten days will not allow you to do all, though, so it is best to minimize the amount of travelling from town to town, and just pick a two or three places to stay in. If it were me I would just do Dublin and Galway as there are a lot of guided day trips you can do from each place. You will see a lot more if you stay in one place longer.