We at times like to do the Kenai with a trip that gets us away from there for awhile. From Anchorage, head up to Palmer, east to Glennallen and south to Valdez, two or three days is good.
Then take the ferry over to Whittier, some nice boat trips out of there if interested, then drive through the railroad tunnel and turn south to see more of the peninsula. We like to stop at Hope, one of the first gold camps in Alaska, kind of quaint and quirky, but fun. Then on south to Seward or to Soldotna. You, as you know, have to do some back tracking on the Kenai. In Seward, there are also several real nice boat trips to see the wildlife and to view the glaciers in that area, etc. After a couple of days in Seward, head on to the towns of Kenai and Soldotna, both can be crowded during the salmon runs and then wander on down toward Homer, drive out on the spit, out the East End Rd, great views.
Then based upon how many days you have remaining in Alaska, start heading back toward Anchorage. The Native Center is very worthwhile, IMHO for a few hours, Earthquake Park has lost much of it's appeal to us since it has grown up since the quake of 1964 did so much damage in that area and was highly visible for many years after the quake. Drive out to Lake Hood and watch the float planes land and take off, we like to take a picnic lunch with us, usually burgers, etc from the Arctic Roadrunner, Drive up some of the roads to the east of town to get a good view of the Anchorage Bowl. Lots of great photo opps in the area. Keep in mind that Anchorage is just a smaller version of Seattle, nothing much Alaskan about either town, IMHO Some good hikes and bike trails in the Anchorage area, bikes can be rented in town if interested. For evening entertainment, Anchorage has something or somewhere for every taste or lack of taste.
Stop at the visitor's center in the small towns on the Kenai to pick up brochures and to inquire about local evens going on that they recommend