www.imdb.co.uk tells us that location filming was at Dublin Castle but, apart from the distinctive round tower, I can't match pictures of Dublin Castle with what we saw on screen. As these were all static short shots I wonder if they may have been a bit of photographic trickery.
Lismore Castle would be in county Waterford, very scenic part of country and worth seeing. If you have the "readies" you could bring a party to stay there!
Definitely Lismore, full page article in TV Quick regarding the programme...Lismore castle, belonging to the family of the Duke and Duchess of Devonshire :o)