I tried a search for you on a few airline sites and travel sites and had the best luck with orbitz. they have a new "flexible search option" that allows you to search for the cheapest flights in a 30-day period for your dept and arriv cities (so you could just search for June), or you can search by when you need to return and it'll give you different options. That might be your best bet.

I hope something fun takes you from LAX to the deep South in June!