Disneyrunner,
I'm making my fourth June trip to Disney after enjoying the fall the last couple of years. To my memory, it's lighter crowds than July, but heavier than late September. You'll find prices, lines, and weather reasonable. There is a pretty good chance of rain most afternoons. Overall, we find it a good time because it's after Spring Break and high school class trips, but before the end of the school year. You're getting close to Gay Week, but you're missing the bulk of it. We'll be hitting right in the thick of it, which means we'll avoid MK Saturday due to crowds and PI Friday and Saturday nights. No biggie. Just know the Gay Week crowd is on the young side and therefore loud. It's not as bad as spring break, but the bars do hit capacity. But beyond your first two days, your crowds should be pretty mellow.