I used to work in Wales (as a neutral) and can assure you that the north and south are split not just for touring convenience! And those in the middle smuggly sit and watch the squabbles, especilly those over who speaks the real welsh.. But there is a genuine issue of the topography dividing the country and reducing long distance travel options. The Cardiff-Holyhead trains which the welsh government promote as unifiers actually spend nearly 2 hours in England to get around the hilly parts! And as far as I know there is still no fast bus to compete with those trains - but there is a road which could be Wales' answer to Route 66 (but narrower and with more bends and only 190miles long). It's called the A470 and goes from the parliament building in Cardiff to Llandudno, search Google and Youtube
The north has the mountains and the best castles and easy day trips to Chester and LIverpool. And easy access to Manchester airport.
The south has the more recent (UK standards!) history, and some decent beaches, and more chance of dry weather. And the scenic areas that sweep around to the north of the Newport-Cardiff-Swansea industrail belt. It has Cardiff airport, but that isn't saying much but there was the occasional flight from Canada. It is fairly easy to reach from Heathrow. Go to the far west end for St Davids - but work out carefully how to do that.
The middle has some fantastic beaches, and often has weather suitable for them. Real welsh culture and language, small villages and some vey nice semi mountainous scenery. Also most of the Great Little Trains of Wales (narrow gauge and usually steam). Also a NATO air force training area (Youtube Machy Loop) which can be interesting to see in use. With Birmingham airport as the most convenient.
North and South actually have connections to Ireland by ferry and plane.
Conwy town is very small but Conwy county includes Llandudno, which is a decent base and not far away. Be very careful with accomodation addresses because the county contains some remote areas, check the postcode in Google Maps.
Caernarfon, yes. Possible as a day trip from Llandudno or as a stopover on a road trip.
Cardiff, definately worth it for the museums and other buildings but don't get stuck there and miss the rest of the country.
You could spend 2 weeks in Wales, you just need to get an itinery in order to fit the topography - and know how you will travel.