Galway airport has just been upgraded so it can now handle jets and long range flights (before you could just fly within the Bristish isles). The Irish market will be flooded with cheep flights for the rest of this year because of changes in the airport authority and airports now being in real competition with eachother.
I'd highly recommend flying into Galway, first off it's a nicer place to visit than the east of Ireland, it's cheeper and better craic. You'll also be avoiding the traffic mess in Dublin if you do leave the capitol by bus.
Is it safe to sleep there overnight? I am a girl travelling alone and I plan to sleep in Galway somewhere - i have no room, and pretty much no money. So if you've been there, do you think airport, train station, or bus station?
"Finishing college in 4 years is like leaving a party at 10pm"
Well I wouldn't sleep in the Bus/Train station and the airporst is a few miles outside town so there won't be much to do out there it's a small airport (I haven't been there in years though) If your really stuck I'm part of couchsurfers.com, I have put up some Americans before.