The University of Wales does not have a base in which these places - Bangor St Davids Cardiff Aberystwyth?

The University of Wales is a federal university in the United Kingdom. Currently, it has five constituent institutions across Wales which include:

- Bangor University

- Cardiff Metropolitan University

- University of South Wales

- Swansea University

- Wrexham Glyndŵr University

So, the University of Wales does not have a base in any of the places mentioned in the question (St.Davids, Aberystwyth).