Two of us will be visiting Dublin, Galway, Killarney, and Kilkenny for about 3 days each and will need lunch and dinner every day. We are on a budget and won't be eating at any 5* restaurants, but we don't want to miss out on the foods that the Irish traditionally eat.
Easily enough if you go to local pubs, and stay in B&Bs. Every town will usually have them, and often with live music in the pubs at night. They're usually friendly, fun, and serve good food.
Source: have been to Ireland twice, first time spent a week travelling around and eating only in pubs, and the occasional bed & breakfast or hostel that served food.
Food included full Irish breakfasts, Irish stew, black pudding, coddle, and so much more, for a list to get your tastebuds watering, have a look at the Wiki page for Irish dishes.
EDIT: realised you also asked the rough price. I went a few years back, but a similar thread on Thorntree says around 10 Euro per meal which sounds fair from my memories.
Many hotels or B&Bs will serve breakfasts (mostly with a choice of either a traditional Irish fried breakfast, or cereal/pastries). Probably just as good as going elsewhere. Sometimes hotel breakfasts can be expensive for what you get, but unless you know a local cafe selling breakfast, a hotel breakfast is probably your best bet.