One real gem is Kenai Lake. It drains from both ends, one toward Seward and the other toward Kenai. There is an excellent campground at Quartz Creek (don't expect it to be quartz like...it's silty till later in the summer) The lodge near the campground used to have great pies. In Cooper Landing just a few miles south you will find numerous rafting guides. The river calm enough for small kids to enjoy the float and you won't find better scenery. Great mountains and aquamarine water. Very good chance of spotting wildlife too. You can see the Russian River salmon fishery with elbow to elbow anglers for a mile.
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There is a second campground up Quartz Creek and when the sockeye come in that is an excellent spot to view spawning salmon...and maybe a bear, keep that in mind. You really want to keep track of the kids in Alaska, the wildlife, the deceptively fast water, the distance from help.
Another spot is the Russian River Campground where you can walk down to the river and try to see salmon moving by...or maybe a bear. From there I'd take a quick look around Soldotna and Kenai, the mighty Kenai River, pickup some pastries at The Moose Is Loose in Soldotna, and then head on south to Ninilchik (don't miss the old Russian church on the bluff)and on down to Homer. The boat tour over the Hailbut Cove is nice. If you are going to do more than drive for your whole vacation, you won't have time for much else. I'd still urge you to pick north or south out of Anchorage. I lived up there for 20 years and have spent a lot of time visiting and I still don't feel like I more than scratched the surface.