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There is a great little museum in a conserved tudor house in Kilkenny: Rothe House on Parliament Street. There is currently an excavation of the tudor merchant's garden which was lost and concreted over during the last century. The gardens will be reinstated to create a renaissance garden due to open in september. I saw a tour of the excavation and it was great.
Also a lovely modern museum in Galway city, in through the spanish arch.
Here is a link to a site with great information about many of the museums around Ireland.