Travelling outside of Ireland into Europe also depends on the passport you hold, but since you had to obtain a visa for Ireland, I would assume you need a visa for the UK and other European countries and since it's a single entry visa I wouldn't risk leaving the Republic. From personal experience I wouldn't be so confident about going over the border into N. Ireland without travel documents. I tried it in 2004, when there were "No border controls" and as we got to the border 2 immigration officials bordered the bus and I had no documents on me, thankfully I was able to sweet talk my way out of it and not get deported.
Stay in Ireland and explore the beautiful country!