Hello!

My friend and I are going to Ireland for the first time for both of us at the end of the month for 6 days/nights, and I would like your thoughts and suggestions on our trip. We are 2 girls in our 20s, and are looking to do a good balance of the cliche, touristy stuff and real Ireland while staying as low budget as possible. We want to rent a car so that we can stop at all the cute places along the way. Here is what we have planned with our must-dos. The flights are booked, but that is all right now. Your advice on any of it is welcome.

Days 1/2 - Dublin (Guinness tour, Jameson tour, Temple Bar)
Day 3 - rent car and drive to Cork (Blarney stone)
Day 4 - drive over to Galway (not sure what to do there, but several friends recommended it)
Day 5 - spend the night in a castle hotel (maybe Clontarf)
Day 6 - go back to Dublin to fly home in morning

A few specific questions:
- Which castle hotels are best (but not outrageously expensive), keeping in mind that we can put it anywhere in our trip depending on location?
- Does it matter if we do Cork or Galway first?
- Day 3 is a Sunday - are we going to have issues with places being closed?
- Any fantastic bars/restaurants we should try in these cities?

Thanks in advance!