Tour Anchorage...If you want to hike and avoid the pedestrian experience of Flat Top then find your way up Campbell Airstrip Road to
Basher Road trail head. This trail is a less developed "single track" until it joins the main trail to Wolverine. Head up Wolverine Peak for great views of town and look over the back side to see glaciers and stuff. There could be sheep up there or some moose along the way. This trail has a lot of muddy spots on the narrow trail, but with how little snow we have this winter it may be pretty dry next summer.
The Anchorage Natural History museum is decent and takes about half a day to go through. There also is a Native Heritage Center just at the edge of town on your way north.
When loitering downtown you want to find your way to 1001 W 4th Ave and check out the Roosevelt Room in the back of a little tourist shop, unless you hate guns, history, and clutter. I think of the place as the front half being grandma's and the back half being grandpa's, if they were the coolest grandparents on the planet. The store shares the entryway with a coffee shop so stay to the left.
I think you would be better served to go from Seward to Soldotna bear viewing then head north. Your proposed schedule puts you in Soldotna/Kenai at the start of dipnet season on the Kenai. It is a sight to behold, but I would recommend avoiding it if you can. There will be a wreck on the roads every few days that shuts down travel for a few hours, or at least backs it up for a few hours. Hard to plan around that, but its normal. You also could be looking at a 12 hour day behind the wheel from Denali to Soldotna. There will be construction delays and other traffic issues along the way slowing things down.
Your Seward date is right after the Mount Marathon race and town could still be packed with the recovering folks. Its a huge party weekend, so there are hoards of people there for more than just the foot race. But then it could be a ghost town as everyone is headed home on 7/5, some still drunk.