Is there a “centralized” place in Wales that’s a good base for see parts of northern and southern Wales? Trying to decide if we want to base ourselves in one region or other if we only have 4 days or so.

unfortunately there isn’t. It’s a large country with lots of mountains an very rural roads. With just 4 days you’ll need to pick one or the other. Both are great but the north might just tip the scale

What are you hoping to see and do In Wales? Will you have a car? When?
Does the four days include getting there and back? And from where?

North (west) Wales, especially Eryri and even more so Yr Wyddfa are vastly over touristed, as is Conwy.
Whilst it used to be the most "Welsh" part of the country that is less so now.
The southern part of the park is a bit quieter and gives you Cader Idris, and Harlech Castle as well as towns like Machynlleth.

Even Northeast Wales is popular now, thanks to Wrexham FC and the TV series around it.

Central Wales has gentler hills, but lovely coasts, interesting towns, old gold mines etc etc.

South Wales has a huge range from Cardiff through the post coal mining Valleys, to Swansea, Mumbles, the Pembroke Coast (little England beyond England), and Bannau Brycheiniog (Brecon Beacons).
Old castles, ancient Abbeys, scattered throughout the country.