Not quite. Scottish, Northern Irish, and Channel Island banknotes are not legal tender in England and Wales. (They are also not legal tender in Scotland, but let's not go there.) They are, however, quite widely accepted in England and Wales (including at all major stores, railway stations, airports, etc.) and you should not have any major issues with them.

As mentioned above, the Republic of Ireland uses the euro, and sterling is not accepted (with the exception of airports, department stores, and tourist shops, but generally at an awful exchange rate).

I am biased in that I am from there, but go to Cork. Not for nothing was it on the Lonely Planet 10 places to visit in 2010. The city is very welcoming and friendly. I won't attempt to list the places to see as you can find that elsewhere.