There is an ice-rink down in the Bay as Cardiff Devils play there.
http://www.thecardiffdevils.com/arena.asp
has a rough guide on how to get there. Not really sure how close that is to the rest of the Bay, but if it isn't too far out then there should also be plenty of other stuff to do around there like in the Red Dragon centre, plenty of nice (cheapish) places to get food or coffee/drink.
http://www.cardiffbay.co.uk/whatson.html