My wife and I are traveling to Canada from Ireland (We are Irish citizens). We would like to visit Seattle in the USA for one night. Will we need a visa? If we do where do we apply?
Are you going by land or by plane or boat?
If flying or going by boat you will need to apply for an ESTA as you are Irish citizens, Ireland is a visa waiver country. Certain ferry crossings count as land crossings though which I have pointed out further down in my answer.
If you are going by land you won't need an ESTA. You will be given an I-94W by the CBP officer when you get to the border.
If you are a citizen of a VWP country, and you are traveling by land to the United States, you do not have to apply for ESTA. If you are coming to the U.S. by air or sea, you DO have to apply for ESTA. If you are not a citizen of a VWP country, you are required to have a visa, and therefore ESTA does not apply to you.
Edit: as Henning Makholm pointed out
VWP citizens do not need an ESTA to travel on the ferries between Vancouver and Victoria, BC and Washington state. They are treated as a land border port.