Is English spoken widely in Ireland?

As others have said, don't call the language Gaelic, call it Irish. If you must say Gaelic then note that the Irish and Scots pronounce it differently.

If you want to specifically refer to the bit of the island which is not Northern Ireland then say The Republic (of Ireland) rather than Southern (Ireland). Better still, don't.

Learning Irish is hard, way harder than French, Spanish, or German. For a start the spelling is very complex.

If you are unlucky you may encounter the occasional Irish only sign. I got stuck in a small road once because the sign which said: "Road suitable only for horses", was in Irish only. However, you will be a remarkable linguist if you learn Irish well enough to understand that during a short holiday.

As Todd says, you will hear a few Irish words, e.g.Taoiseach, though I think tea shock is a closer approximation. Gardaí is police and you will commonly hear them called "The Guards".

Relax, have a Guinness or three and a couple of whiskeys (note the spelling) and concentrate on having some fun.

During a recent trip, the languages that I heard, in order of frequency, were: English, Tagalog (Filipino), Polish, and Irish. Apart from the TV, the only Irish was my mum talking to the band in the pub after a couple of glasses of Jameson.

As others answers say, English is by far the dominant language, but one use of Gaelic is reading signs in Gaeltacht regions, which are officially Gaelic speaking. While the people there speak English as first or second language, most signs are in Gaelic, including traffic signs.

Gaeltacht regions are scattered over Ireland. Much of the rural area around Galway, including Connemara and the Aran Islands, is Gaeltacht.

I've lived in Ireland all my life (now in my 40's). I've never met any Irish person who could not speak English fluently. Thats including several holidays in the Gaeltacht (Irish speaking area).

As a resident of Ireland, the only time I hear Irish spoken in conversation is when on one of the small west coast Islands, and even there it is uncommon.

99.5% of the media (TV, newspapers, cinema, books, etc) are in English.

I learned a little Irish-Gaelic at my local Irish Club where we had lessons. I taught my son a few phrases and when he said 'Conas ta tu?' (How are you), to his Italian friend Eduardo, he understood it and answered in Italian, as the Italian translation is Com e sta (I'm not sure of the spelling). There aren't many similarities, but I love the fact that many European languages use similar words, for example; the Irish word; Seomara,(room) doesn't look much like the French word Chambre, but the pronunciation is similar. Learning a bit of Irish-Gaelic, made me realize why Irish and Scots people often use a different word order to the English, even when they are speaking English. There are lots of little differences in the way they word things in Ireland, such as on road signs, instead of 'Give Way' they say 'Yield'.