I need 4 CHEAP airline tickets. Which site is the best to purchase tickets from? 2 adults, 2 children (4/2). Traveling mid week to mid week. Are there days that are cheaper to travel on than others? Thanks for any help, as we are on a tight budget as most people are and I'm trying to figure out how to have some sort of a vacation for us.

check these first
www.southwestairlines.com
www.jetblue.com
www.flyi.com

then check these mainstream comparison sites
www.expedia.com
www.hotwire.com
www.travelocity.com
www.orbitz.com

*generally week travel is less expensive with Saturday night stayover, but companies like Jet Blue you buy one way tickets. Sites like expedia you can choose travel date and click '1 day before ok' or '1 day after ok'. They also have fairwatcher deals. If you want to travel to Phoenix for example, you type that in there and it will email you when fare goes below say $120.
Children under 2 fly free