I have been to the tourist office,and have come up with loads of stuff for you.
A day trip by ferry to the Aran Islands (one of those places that everyone says you must visit, but we haven't yet)
Westport House and Country Park, www.westporthouse.ie. We go as a family every couple of years and bring a picnic.
Sight-seeing cruise on Irelands only fjord...the brochure says 'It's magic will be the high point of a rainy day'. www.killarycruises.com. That would be quite close to Tullycross.
Brigit's Garden, beautiful themed gardens reflecting celtic festivals. And there's a children's discovery trail. www.galwaygarden.com
Glengowla Mines. This would be quite close too.
There is an adventure centre with canoeing, abseiling and that at Delphi, near Leenane, but your kids might be a bit young.
In Galway city, in Salthill, there is a funfair every summer, but it's expensive. Then there is the Prom, which is a walk by the beach, with amusement arcades and that. if you keep going you come to the Atlantaquarium, and there is a playground just past that.
The village of Cong is IMO a must see. You can wander around the beautiful wooded grounds of Ashford Castle, on the shores of Lough Corrib, and through the terraced gardens (but for God's sake don't pay at the gate, either go in the back way, or say you are visiting the Murphys and go in the main entrance....honest). From the pier at the Castle you can get a boat trip to Inchagoill Island, where you get to wander around and see an ancient church. In the village, Ryans Hotel has good food, at reasonable prices in the pub, you can feed the ducks on the river, (by the shopand petrol station), and the children will love to climb around the ruined monastery.
I know I sound like a brochure, but it really is great, though I'm biased cos I grew up there. I brought the kids to Ashford for a walk today, and they had a ball.
Keanes pub in Maam is really nice too, good sandwiches and a lovely atmosphere.
And naturally all the pubs will sell tayto crisps,AND red lemonade.
In Clifden, the Station House hotel pub has very nice food too, and is family friendly.
HTH