You won't be able to use the cottage as a base unless you are willing to stay overnight elsewhere. Although Ireland appears small to be able to return in a day might be a bit optomistic. My favourites were a Blackcab tour of Belfast,
of course the Giant's Causeway and the Ring of Kerry is breathtaking. Did a nice walking tour in Londonderry also.
I also suggest Newgrange, just outside Dublin. A pre-pyramid ediface built for the solstice like Stonehenge but very different.
I am your age and travel alone and you should have no problems there. Will you be driving? I don't as hubby won't allow me to drive there and tourist accidents are huge, narrow roads etc. Also because I was alone the one time I thought to heck with it I will rent a car so booked on line before I left as it is cheaper, however, once I went to the dealer at the airport they wouldn't rent one to me as I was on my own and didn't have a celphone with me.
I find the National Express Bus Lines and the Railway very good and pick up local tours either through
the Tourist folks or what I find to be better tours (no shopping) www.hostelworld.com
Sligo has standing stones, I've only ever seen on TV and I think a car might be necessary.
The Railway has day tours as well, so you could look into those.
Take white tissue paper and black wax crayons for grave inscriptions that aren't clear in photo's.
Dublin has the National Archives and the National Library has a genealogist you will explain what is available and where. They have RC records on microfilm. Plan on spending sometime there is you are going. Watch for closures for
Bank Holidays - our long weekends.
Going and leaving from Shannon should be fine although I've always gone to Dublin but usually pick up a fare from the UK when I visit relatives.
I love the sound of the cottage. Hopefully you aren't far from where you have good transportation links if you aren't driving.
I'm going over in September to a genealogy type conference and will be flying Vancouver-Toronto-Dublin for the first time.