Maybe 3 hours if your intention is to get from A to B as fast as possible, during the night with no traffic, but I don't suppose that's your plan! If you want to stop off at a whim because you like the look of a place, you could double the travel time.
'castle' hotels are generally a bit pricey, but don't let me stop you checking them out on the web. The Delphi centre has a good reputation.
If you meant 'end of March', you are already here!, if you meant 'first weekend in April' you have hit Easter, and many places will be closed on friday. Just make sure you have the makings of a picnic with you in the car, and you will be ok.
The suggestion of the buses from the airport is really good! but you might then need a car while in Galway - its a big county with almost no public transport.
Have fun!
p.s. just noticed that the rail line from Limerick to Galway has been re-opened, travelling via Ennis and Gort, so there are several nice stop-off options there, if you wanted to slow down and spend a few days in the West.