Hmm that's a good question, i'm going to be there June 3-8, so I could definitely post back about wait times etc. when I get back. I'm not exactly sure as to how busy it would be since i've never been to Disney in June. On one hand, school is out and more people might be at the park, but I was there last month and it wasn't too bad depending on what time of Day you went. To ride Mission: Space is always good if you're a single rider, because wait times are always the shortest for single riders.
Also, don't forget Disney's wonderful Fastpass! Usually after getting one you only wait about an hour before you can ride the rides, then you only wait like 10 min tops in the Fastpass line! If you aren't doing either of those for some reason, I would say later at night and early in the morning closest to Future World's opening are the best times to go! Have fun!