Somewhere in the Alaska subforum (the state, not the airline), I think I had a nice long list of the top 10 (or so) restaurants in Anchorage along with a brief description of each one. You might find it if you search--although I may have instead posted it on another site which has now been taken down (in which case it exists solely on my now-virtually-defunct-but-waiting-for-repair laptop). For now, here are my recommendations:

• Simon and Seafort's - You'll feel like you're walking into an upper-class saloon out of the old west as you dine on fabulous dishes from meats to fish (try the halibut cheeks crusted in Parmesan asiago cheeses and braised in a beurre blanc sauce) above a stunning view of Cook Inlet.
• Orso - Fusion Alaskan-Italian in a very nice, quiet, almost romantic setting, it features great seafood and trendy Italian-influenced dishes (that's about the best description I can come up with)
• Glacier Brewhouse - Owned by the same people as Orso's, its atmosphere is a bit more casual and geared towards grilled meats, wood-fired pizzas, cold and hot sandwiches, and, of course, beers brewed right on the premises (you can see the tanks behind the bar area).
• Sacks Cafe - Tucked on a side street a few blocks behind the bigger, famous restaurants, it's much less well known but serves great light, fresh dishes.
• Cafe Croissant - A relative newcomer, Cafe Croissant is Anchorage's best attempt at French (or French-influenced) cafe food, and they do a pretty dang good job. Excellent soups and sandwiches and things, and definitely try some of the pastries for dessert!
• Double Musky - A ways south of town, this restaurant serves Cajun food straight from Louisiana. Try their famous peppercorn steak.
• Bear Tooth Grill and Theatrepub - Same owner as Moose's Tooth but the menu is completely different (though they share microbrews between the two). There are actually two halfs to this restaurant: the Bear Tooth Grill, featuring everything from burgers to enchiladas, and the Bear Tooth Theatrepub, which has a smaller segment of Moose's Tooth-style pizzas and appetizers. The real draw of the Theatrepub side is that you can order your pizzas, breadsticks and beers in the lobby and then go into the theater and watch arthouse, foreign and second-run flicks while you wait for your food to be delivered to your seat. A unique experience, as far as I've been able to tell.

I know there are others, but these are the ones that come to mind right now. I'm sure some folks will post others or critique my choices...