Limerick

Limerick City is one of the largest cities in Ireland. It is 200 miles from Dublin and is accessible by bus from Dublin (3h30 hours and 10 euros), by train (a little faster, but they are 30 euros), and also by plane from Shannon International Airport. Shannon Airport is a main Ryanair hub, so you should find cheap flights if you visit this city.

Most people come to participate in the International Erasmus program, or simply because of they're able to get a cheap Ryanair flight. The city does not have very good reputation in Ireland, because it is a former industrial port and as such it suffered greatly during the economic downturn and the consecutive closures of factories in the region.

I would also recommend the shopping area in the city centre.