Are your dates fixed? That is, are you looking for a trip anytime in June, or just for one exact set of dates? Sites like skyscanner.com will let you search destinations and then look at prices over a whole month, to help find the cheapest days to fly.
Some budget airlines -- Southwest in particular -- don't show up via booking sites like expedia or kayak. So if you haven't already, check Southwest directly, along with Frontier, Spirit, JetBlue (although I think most of those do show up on the aggregator sites). BUT, before you book a flight on any airline, double-check its baggage allowance! Frontier in particular is obnoxious about making you pay for pretty much every bag, which means their "cheap tickets" can come to a whole lot more if you want to bring a change of clothes. Southwest is good though.
You've got a ton of time before this trip, so it probably would make sense to wait a bit and see if cheaper tickets come along. There isn't really a magic window when prices are guaranteed to be cheaper, so I know this can be nerve-wracking, but you're still verrrrry early. I usually find my best deals in the 3-6 month window before a trip (but that's purely anecdotal, of course, and depends a lot on the destination). You could also check discount fare sites (airfarewatchdog.com, secretflying.com, probably many others) to keep an eye out for special deals and error fares. You can sign up for fare tracking with some search sites too, if that's easier than constantly looking.
