It is actually in the midlands of Ireland, close to the centre
of the country, so it is not in the north, south, east or west of
Ireland. It is in the Republic of Ireland, which is sometimes
incorrectly referred to as "Southern Ireland" or the "South of
Ireland".
Related Q&A：
Is Mullingar north or south or east or west of Ireland？-Oh, well, Mullingar is located more towards the center of Ireland rather than being strictly in one of the cardinal directions. But if you had to be specific, it's kind of to the west of the country. It's not too far from the western coast. So, you could say it's in the western part of Ireland. Isn't that interesting? I hope that helps clear things up for you!
