Ther are several zoos in Wales, but generally of the smaller variety! For big animals, the Welsh Mountain Zoo (Colwyn Bay) in the north and Folly Farm (Begelly, Pembrokeshire) in the south are the best bets, still not massive places but worth a look.
That said, there are some much bigger/more significant zoos not far over the border - Chester is just barely in England by the North Wales border and Bristol is close in the south.
Whereabouts in Wales will you be? Its geography is such that travel across into England is often easier than trying to get from north to south.