I've never played up there, but my brother lives in Anchorage, so I've been up a few times, including this past summer. There was a course on the military base that they closed a couple years ago called Eagle Glen. Ship Creek, which runs near downtown, ran through the course, and a lot of people go Salmon fishing in the near-downtown area. Just above the fishing area is a dam, above which no fishing is allowed. You can walk along the top of the dam and see all of the fish that have made it upstream regaining some energy above the dam. When I was there about 12-13 years ago, you could also see about a thousand golf balls that had come downstream from the course. Must have cleaned them out after the course closed, because I didn't see any last summer.
We did see a funky little nine-holer just outside of Healy called Black Diamond that looked fun if you're heading up toward Denali. It's about 10-15 minutes north of the park entrance. It's also just down the road from 49th State Brewing, which I highly recommend. They have an Anchorage location as well, but there are better breweries in Anchorage (Midnight Sun, King Street, and if you like sours and wild stuff, Anchorage Brewing).