I'm going to bang the drum for North Wales!
Some really impressive castles at Conwy, Caernarvon, Beaumaris.
Stunning mountain scenary in Snowdonia and pretty countryside in Clwyd and Denbigh.
Mountain railways and historic slate mines to explore.
Traditional seaside resorts all along the coast. (Avoid the resorts right at the north, eg Rhyl and Prestatyn unless you are an admirer of a caravan park! That said it's where I spent weekends as a kid so I have a soft spot for them!)
The pretty, and slightly mad, Portmerion Village. Beautiful and interesting Plas Newydd house.
Canals and the astounding Pontcysyllte Aquaduct.
For the more active minded mega long and fast zip wire rides through the mountains, the world's first (?) Inland surf lake and trampoline parks inside a mountain.
Enough to keep you going for days!
Wales might not be well known in the USA but it is popular with local tourists so it isn't going to be quiet in peak season. Avoid the coast and castles during sunny weekends but it isn't hard to get a bit off the beaten track in the mountains to get away from the bigger crowds. Anglesey also tends to be a bit qureter than the main land.
Wales has its own language and culture which is interesting and worth enjoying. Welsh is commonly spoken as a first language in the north but everyone does speak English. All signage, including road signs, are in both languages.
Pronunciation in Welsh is very different to that in English but the locals are use to visitors massacring their language.:-)
The Welsh love their music and poetry and competitions or Eisteddfod are regularly held in the summer. Also look out for sheep dog trials.
One thing I will say is that whilst people are friendly they are perhaps less outgoing than you might have experienced in Ireland.
Generalising, it is quieter, less in your face, than in other Celtic countries. The fact that people actually speak welsh is off putting to some (slightly ignorant) visitors who seem to find it rude. This is not the case, it's just what people actually speak, it's not done to alienate visitors.
People, especially in the north, can seem quite reserved, but you won't find a friendlier people when you get past initial reserve.
You could combine a trip to Wales with a sometime in the border counties between England and Wales. Some of this is a little known area even for UK locals.
Chester for roman and medieval architecture, Hay on Wye - the book town, Ludlow for amazing food. The area around the "pottery towns" has some of the best ceramics museums in the world. Ironbridge for historic industrial architecture.
There is loads to see and do, please come!