Hi Petra,
There are so many Traditional Music pubs in Galway City...it's actually a heard questions:>)
Here is a list of some: Music Sessions
I would recommend you check in Taylor's Bar.
Another place to check out is the Roisin Dubh on Domminick Street.
Connemara...well a short bus trip from Galway itself will take you out to Spiddel. There is a great pub there called Hughes. Mighty sessions. Strong Irish Language area.
Best way to find out what's happening though is to ask some of the Musicians at the sessions when you get there.
I hope you and your Friends have a wonderful Trip.
Jude

Maybe this thread should go up to visit the Music section to see if any Folks in the know can give better info? Thanks Mudcat Elves:>)