Students tend to go to their nearest one unless the course they want is not offered there.
Bear in mind that many Irish students live at home or go home most weekends
@Decorhate I'm assuming you're not Irish?
I'm Irish, studied at 3 different Irish universities (undergraduate & postgraduate study), and have worked at 4 others, including now (Maynooth University).
So have a good understanding I think!
Decorhate is broadly incorrect here.
Firstly, many Irish students don't have a university near to them! This is true for large swathes of rural Ireland. The distance to travel home wouldn't enable students to go home each weekend.
Secondly, many students do choose universities based on how well-regarded a course is. I chose my course & university on that basis.
It is correct that in Dublin, many students continue to live at home, if they're from Dublin or the wider area, and similarly for MU, but equally those universities have many students from outside Dublin who will stay at weekends.
So disregard that entirely. There'll be plenty of people around at weekends!
Moving on to how international / EU students fare, in my experience, they are well provided for eg designated offices to offer support, societies & separate provisions like an orientation for overseas / international students. So I'd have no worries on that basis.
A bit cliched, but Ireland is, overall, welcoming, and overseas students generally love it here.
Regarding offers, each university sets out the criteria for entry to their course from each country, so check the websites of any university you are interested in.