Besides Phoenix and Sedona....
By all means take a day (or a few) and spend some time in southern Arizona and experience the Sonora Desert, about as far from the Irish countryside as you're likely to get. The best places to experience the desert are the two units of the Saguaro National Park as well as the Arizona-Sonora Desert Museum (actually more of a zoo).
A little bit farther afield are Kartchner Caverns and Kitt Peak National Observatory. Again, you're not going to find anything like these in Ireland, and visits to these sites will help make the most of your trip.
AZBuck