The Gaeltacht areas are those official areas where the Irish language is the main community language (as opposed to English). Even then, the official borders are old, and include areas that now speak English.
People in the Gaeltacht will be interested in speaking with you, for sure. In many of the Gaeltacht areas, for example, they are used to having people come and learn. There are numerous education centers in those areas.
But here’s the thing. It’s up to you to start speaking Irish with them. By default, they will most always speak English to someone who they don’t recognize (that’s in Eoin’s experience anyway). Get ready to say “Dia dhuit!” when you walk into their shop.
Here’s a nice tip: trying staying with an Irish family. You can do that even if you’re booking a B&B. You’d just have to ask first of all which language they speak at home. For example, we always stay at http://www.sleaheadfarm.com in Kerry, because Caitlín speaks Irish.
For the urban areas, you’ll really have to seek out Irish. If seems like certain parts of Belfast has strong Irish spoken. You’ll find it in the other cities too, but you’ll need to know where to look. Actually, I suggest seeking out people through the internet if possible. One idea is to find Irish groups on www.meetup.com .