This local dog park, located near Alaska Pacific University, is a popular destination. There are both on-leash and off-leash trails, depending on your preference, as well as great places to throw a frisbee or ball. The lake itself is 28 acres, and dogs are welcome to jump in for a swim. There's a beaver lodge located on the southwest end of the lake, and beavers can often be seen there (though you and your dog should be respectful and give the beavers plenty of space - they are not afraid to guard their territory!) If you take the trails around the lake, you can see where beavers have gnawed away at tree stumps to build their lodges and dams.
As a part of the Chester Creek Greenbelt, University Lake Park is secluded from the bustle of Anchorage, and yet is easily accessible. The park also has picnic tables, benches, and in the winter, dog mushing.
There is a parking lot off of Elmore Road, but parking is limited (you can park for a maximum of 2 hours).