General   (General discussion, talk about anything.)

ena, let's see if 'we' can give you some help.

Your question: 'Where in Ireland would you recommend for extended visit/touring around?'

By now, some posters have offered you a choice of places and with some additional information, which I hope you find useful.
Of course, like always, it comes down to how large the country is, how much time you have and what do you really want to do during that time.

For me, I want to see things which are interesting, historical, beautiful, to see lush landscape and to see and experience great culture, to be part of that atmosphere of local life...
Additionally, I also want to have the time to relax and the time to enjoy some places - I don't want to be jumping in-and-out of the car and rushing off to the next place, only to spend a few hours trying to see and photograph everything that the tourist guide etc tells you 'this is a must.../got to visit this...'.
Ireland is a large island and some parts aren't engineered for speedy travel. In other words, the highway system does not equal the English highway system; simply because in many parts, if not in most, it does not need to. So, do not expect wide, long motorways stretching across every part of Ireland. In parts, travel can be slow.
I was in and around the Cork and Kerry area in the last quarter of 2019 and enjoyed my stay there very much. There had obviously been some highway work done: new surfacing and new construction. There was a dual carriageway, which looked new, and which stretched quite far; this allowed comfortable, easy and time saving travel.
Regarding what I saw and what to see in the area mentioned, the choice is vast. There is wonderful landscape and beautiful villages. Some of the coastline is breathtaking: dramatic cliffs, crashing waves, misty mornings, beautiful rainbows with vibrant colours, long sandy beaches... On the opposite side of what to see, I found Dingle beautiful, relaxing and a total contrast to the sights and sounds of the cliffs. This small port town is full of character, with its calm coastline, sailing vessels, fishing boats, old streets, old buildings, architecture and brightly painted buildings (pubs, shops, some houses) it is definitely worth a visit. A very nice place to spend a few days in.
Now, here is what we all have to bear in mind: stretching across to the other coast you have Dublin, which I have spent time in and can definitely recommend visiting. But, the distance is great (possibly around 350km) and will obviously take time. On a positive note, you can stay in Limerick for a number of days or even one week to break up the journey. Limerick is another one of those places which is 'a must' and obviously so, because this is one of the largest and oldest cities in Ireland.

Sorry for not answering your other question about 'common travel/border', but I think that I have typed enough for now. But, just to finish, I can tell you this: I needed my passport and on arrival in the stated year, there was passport control and I had to show my passport - and, so did the other visitors to the country 'Ireland'.