Hello, James, and thanks for dropping by planDisney, where dreamers of all ages are welcome!
James, as a guest who is also planning a visit to the Most Magical Place on Earth this summer, I appreciate this question. This June, you'll find a few special "extras" such as:
- 
Disney After Hours     At 
Disney's Hollywood Studios, this event takes place on June 7, 14, 21, and 28
     At 
EPCOT, this event takes place on June 1, 15, 22, and 29
     At 
Disney's Typhoon Lagoon, this event takes place on June 3, 10, 17 and 24
-Pride Month
     Throughout the month of June, you'll find 
special merchandise and 
delicious snacks at all four theme parks, 
Disney Springs, and at a variety of locations at Disney Resort Hotels.
- 
EPCOT International Flower & Garden Festival     Continuing through the month of June and included with your park ticket to EPCOT, you'll find gorgeous topiaries, garden-themed treats all around the park, and beautiful photo opportunities.
Now, James, while not specific to the month of June, I'll encourage you to check out 
THIS PAGE that shows the Enchanting Extras Collection. If you're looking for special opportunities, tours, and experiences beyond the parks, you'll find all that and more on this list.
James, I hope this helps as you're looking ahead to June at Walt Disney World! If you have any additional questions, please come on back to your new pals here at planDisney. 
Lauren