Yep, best to avoid the Seward Hwy on Sunday afternoons in the summer. Bumper to bumper can start 50 miles south of Anchortown. Last week of June can be, but not every year, not the best fishing. First run of sockeye is tailing off and the second run has not come in yet. Try Ninilchik and Deep Creek for kings. Bank fishing for Kenai kings is not very productive any time, they are just too big and the water too fast. Rafting on the upper Kenai is always good for rainbows and maybe some late first run sockeye. When I lived in Alaska the end of June through the 4th was a time to abandon the Kenai and fly out to Illiamna to fish the Newhalen River. Millions of sockeye and some nice rainbows, but watch for bears, there is jet service. The time you are planning is also a great time to hike up past Russian River falls and fish the middle river for rainbows and dollies, but again watch for the bears. I spent a very hair raising night at the top of the falls many years ago with a bear prowling around just outside the light of my fire. Later in summer the grass along the middle Russian is over head high and if there's a trail, you know it's used by bears, spooky. Parks Hwy streams should be good at the end of June.