Twice I've been to the Eagle River Nature Center a few miles (about 9-10) east of Eagle River on Eagle River Road - it dead-ends into their parking lot. There are some easy trails that will take you out to a few viewing platforms out over the river. The scenery is pretty spectacular - there is hiking in the area but this is just a nice walking stop. It's a good side trip for a longer day trip - Eagle River is only about 15 miles north of Anchorage plus the distance out to the nature center. We've seen moose in the area too.
I stopped on Eagle River Road for this pic:
From one of the viewing platforms:
