Students from a non-EEA country who intend studying in Ireland for a period of more than three months must register, after they arrive, with the local immigration officer for the district in which they are living (Garda National Immigration Bureau if living in Dublin). Their passport will be endorsed with the conditions and period of time for which they have permission to remain. Information on what documentation students require when applying for permission is available on the website of the Irish Naturalisation and Immigration Service (INIS).

This means you should be aware of the terms conditions attached to your visa, do you have a copy of the paperwork with you to look over?

This link has useful information on applying for student visas extending your visa

I would make contact with the Garda National Immigration Bureau to ask questions about what you can or cannot do:

This link has information on third level education in Ireland

If I were you I would go to the local library borrow a travel guide on Ireland (or just go to a big book store where they won’t notice you’ve been reading the same book for 3 hours) – make a note of the other major towns/cities in Ireland and if you can afford to, go spend a weekend in them – Bus Eireann is quite cheap for a coach to Limerick, Cork, Waterford or Galway – see how you like them.