Trim Castle fits the bill and is an easy drive from Carton House.
https://heritageireland.ie/places-to-visit/trim-castle/

On gardens, they are more likely to be attached to country houses rather than castles, exceptions would be Malahide Castle (reasonably close) and Birr Castle (90 mins away). Gardens are obviously dependent on time of year as well.

Powerscourt Estate in Wicklow has probably got the most famous gardens in Ireland. The National Botanic gardens in Dublin are also worth a visit.