There are plenty of places to hear and see traditional Irish, Scottish, and Island music and dance, particularly in the summer.
The Benevolent Irish Society hosts many events during the summer from music to food to lectures. Also, there are an incredible number of ceilidhs held all summer long (ceilidhs.ca). You could go to one every night of the week!
Finally, there are a couple of pubs in Charlottetown that feature traditional music most nights. The Old Dublin Pub on Sydney Street and the Old Triangle on Great George Street are two good examples.
I'm sure you will find something right up your alley.
Enjoy your visit to PEI!