Chapter 2: The Road South
The road south out of Anchorage is the Seward Highway. It sounds like you will be up there before Labor Day, which is a pain, as traffic on the Seward Highway is very heavy until after that. Lots of locals going fishing and camping on the Kenai, and lots of tour buses full of GORPs (local name for Groaty Old Retired People).
As you drive south, the Chugach Mountains are on the immediate left and the Turnagain Arm of the Cook Inlet is on the right. It is a very scenic drive. There are a number of observation areas along the Arm, where you can pull off. Occasionally you can see whales along here. Also, the Cook Inlet has a very high tide, and when that tide flows into the Turnagain Arm, it creates a bore tide, a wall of water that can be several feet high and moves very rapidly. Check locally for tide tables.
At the end of the Arm is the Portage Glacier. This is a must see. There is a very good visitor center there, and I highly recommend taking the time to watch the movie. From there you head back up the other side of the Turnagain Arm and then over Turnagain Pass and south on the Kenai Peninsula. Two major potential destinations are Seward and Homer. The former is so-so, the latter is highly recommended. Homer is (was, years ago?) a real fishing village.
Rather than try to provide any more detail, I will refer you to the ultimate must-have for leisure driving in Alaska.
BUY THIS. Period.