I would recommend either Rising Sun or St. Mary campgrounds in the park. Both are close to the "middle", meaning a short drive to several worth while hikes. If you're bringing a big rig in and want satellite service and such I believe Apgar is your only option. Way too many yuppies for me, but I won't judge you either way. Short hikes your kids might enjoy would be Avalanche, Virginia Falls and Logan Pass. Longer hikes that I really like are Grinnell Glacier, Ptarmigan Tunnel, and Granite Park Chalet. Waiting for our kids to be older to go back into Goat Haunt as I hear it is amazing. I don't live in the area, so must defer to DaveC with bugs and fishing. June might be tricky, we go in August (this will be 8th consecutive year) and three years ago there was still 8-10 ft drifts of snow on Logan Pass. We brought sleds and the kids (little and grown up) spent a long fun day sledding down the Logan Pass trail to hidden lake. I'm not a Glacier professional, but feel free to pm me if you have any other questions that I might be able to help you with.