Edinburgh is very accessible from Glasgow. Good train/bus links. Worth a day trip.

fly out to Amsterdam (aug 31-sept 5): would look to take a day trip out of the city; any suggestions would be awesome.
You can quickly reach Haarlem, having some nice canals, parks, shops, restaurants en plenty of musea.
When the weather permits you may check nearby beaches of Bloemendaal/Zandvoort. Both have nice beach and are loaded with cafes/restaurants. When you want to combine: these two beaches can be reached by rented bike from Haarlem.

Go to Galway- its a wonderful place (more "Irish" than Dublin).
Drive from Dublin to Galway is about three hours on a new motorway or you can get a train from heuston station- see irish rail website for lots of time and ticket booking. In fact heuston station is not that far (maybe twenty minutes walk) from Guinness storehouse.
I wreckon
Day 1 (August 23rd) Dublin -Guinness storehouse & wander around the city. (South William street area is the best for restaurants).
Day 2 (August 24th) Early train to Galway- stay in the city- hire a car & drive around connemara & spend evening in one of Galway's brilliant pubs.
Day 3 (August 25th) Trip to Cliffs of Moher.
Day 4 (August 26th) Drive to Shannon- about two hours (or Citylink do excellent bus service- they have a great website-just google them- they also do Dublin to Galway and are very professionally run & go from Dublin city centre).
Go to Shannon at the last minute as there is nothing to see there- Enjoy your trip- this should give you a good mix of Ireland.
If you have a day spare- depending on when exactly you arrive in, you could do a day trip from Galway to the Aran Islands either.

As far as renting bikes go, Dublin bikes is the same idea as Paris- kiosks all over the city that you can rent them from and leave them back at.
If you don't want to go to Galway, you could go to Wicklow- very scenic around Glendalough and you could also visit Newgrange in County Meath.
Make sure you get out of Dublin for a bit of your trip, just to see a different side of Ireland and some nice countryside.