covediver
Contributor
to add to what covediver stated, there is also jetboating up to the Knik Glacier which is incredible (personally I'd rather do that than 20-mile, but to each his own).
Also there is a great guide service that takes people on glacier tours of the Matanuska Glacier. I forget the company name, but they are right there on site near the beginning of the road that goes from the Glen Hwy to the glacier. They have all the gear, and the people are really cool. I took a bunch of visiting relatives on that tour this summer, and even though I've been all over that glacier on my own, I enjoyed myself.
MICA guides just past the Rifle Lodge, look for the yurt. You can make reservations on their website. The guides are great. I have used them the last two summers with visitors to Alaska and have not been disappointed.
There is also rafting down the Matanuska River as well as rafting from Hope (which I understand has some pretty good rapids). Since you are coming in June, you should hit real good weather.
If you are going to do the more popular activities around Denali, make your reservations early.