June is a very good time to go. The hotel prices are in value season until very late June, so if you want to stay onsite, go ahead. Early June is much less crowded than late June due to schools getting out for the summer. A few years ago I went to DL for a day in late June. We went from 8-10 and rode everything that we wanted more than once (Space was closed for refurb). By using FP and getting there early, we didn't have to wait more than 30 minutes for anything. Average waits for major attractions (Splash, Indy) were around an hour. But rides like HM, PotC, and Jungle Cruise were around 15.
Here's a list of rides that you don't want to miss as a WDW vet/DLR noob:
-Indiana Jones Adventure! Just like Dinosaur except better!
-Matterhorn
-Pinocchio's Daring Journey
-Mr. Toad's Wild Ride
-Alice in Wonderland
-Roger Rabbit's Cartoon Spin
-Storybookland Canal Boats/Casey Jr. Circus Train?
-Pirate's Lair. Tom Sawyer Island with a new theme
Rides that are better at DL than at WDW:
-Buzz (you can actually remove the guns, which makes for easier shooting)
-Space Mountain (complete darkness with lots of fiber optic "stars")
-Autopia (Tomorrowland Indy Speedway except 5x better because of off roading and better scenery)
-Pirates (twice as long with 2 drops and tons more scenery)
If you also go to DCA, I recommend seeing Grizzly River Run (disconnected FP helps a ton in the summer), Tower of Terror, Monster's Inc, California Screamin. But most other things either are carnival style rides or are exactly at WDW (Soarin, Bug, Muppet, Turtle Talk)