I did three weeks in Ireland on my own a few years ago. Transport is really easy -- Bus Eireann and Iarnrod Eireann serve almost anywhere you might want to go.
Accomodation can be cheap. If you're looking at hostels, it might only be a few euro a night in places.
The Eire tourist board is really helpful. I went to one of the offices when I was there, and the woman booked hostels for me at discounted prices for the rest of my trip.
While I was there, I went to Dublin, Galway, Cork, Killarney, back to Galway, Donegal, back to Dublin, back to Killarney, and then flew home from Dublin. I did side trips from all of the places except Dublin.
I'm going back to Dublin in April and I'm really excited. I don't really like Dublin, but I love Eire.