I note that there aren't very many Starbucks in Ireland. So I was wondering if anybody knows if there's another coffee house chain (or restaurant chain) in Ireland with free wi fi. I'm assuming hotels charge for it and I don't want to pay for wi fi.

Some McDonalds restaurants offer it, I believe.

Not sure how reliable this site is for Ireland, but it seems to be fairly accurate for a lot of places near me that I know have free wifi.
http://www.openwifispots.com/country...reland_IE.aspx

These guys supply wifi hotspots for businesses - though not all of them are free. Some probably are, others might require purchase for use. But at least it might give you a few options.
http://www.bitbuzz.com/locations/

Not all hotels, guest houses or B&B where available charge and with no end of available accommodation you could make it one of your selection criteria. If there is a spot you fancy that does charge for wifi send an email and ask if they would be prepared to waive the fee as you will only book if there is a free service.

If you go to http://www.mcdonalds.ie/about-us/res...t-locator.aspx and scroll down below the map then click on the counties you will be visiting you will see which McDs offer free WiFi.

All McDonalds offer it, from what my friend Kemberlee says. Many B&Bs also offer it - 6 out of the 7 I am staying at this month have free WiFi. It was one of the things I looked for

Apparently not all McDs in Ireland offer it according to my link. Most do but there are a few exceptions.