Derry is only 5 or 6 miles from the Donegal border Minty. Where in the county is annie's family from? It covers a very big area, is pretty rural so public transport wouldn't be an option unless you can get a relation to pick you up from one of the bigger towns. Fyi, Letterkenny, the main town, is a stag/hen hot spot. If you fly to Belfast, you will still have to get a bus to Derry, ( 2 hour journey). Fly to Dublin and its 4 hours plus by bus. No trains in Donegal as far as I know, they lifted the tracks decades ago. And for the love of God or allah or whatever deity is popular this week, DONT call Derry "Londonderry" in Donegal, even in jest. They'll explain to you why it's nor done and if you contiunue, you'll be lucky if you get away with a few thumps.
On the plus side, Donegal is gorgeous and completely off the main tourist trails. I'd defo recommend hiring a car. If you stay in a small village, chances are you'll get a lock in particularly on the weekend. You won't get Foster's on draught but you'll get Heineken, Budweiser etc for @ 4 euro a pint. ( alcohol is generally stronger here than UK ). The weather is guaranteed to be good the first 2 weeks in June. Will get iffy from mid June on. If you don't believe me, ask any Irish person what the weather is like during the Junior and Leaving Cert exams ( O and A levels), and they will tell you the same. Early June weather for 3 of the last 4 years was topping 23 degrees. The pub grub is of a very high quality generally and is about a third less in cost than UK.
Let me know where Annie is from and I'll check to see if there is any bus link to it ( either private or public)