Welcome to the area!!!!
There are museums around that are FREE as well as the many events that downtown Raleigh offers.
Don't forget the 8th Annual Children's Good News Spectacular (which is FREE) that will be held at the Fairgrounds on August 25th and there will be MANY other back-to-school events between now and the traditional calendar start date of August 27th so stay involved and informed.
Depending on the school your children attend, they often have things for the students to do, that are age appropriate as well.
Again welcome to the area and I hope you and your family enjoy your time here.