You have to try the Moose's Tooth-- you will need to catch a cab there but it really is some of the best pizza anywhere! It's always packed with locals, so if you want a low key, relatively inexpensive and super delicious meal, check it out. There's a place right next door (Kinley's) that was also very good (and has free WiFi) when I was there. A little fancier but still very "local".
If you are wanting to stick to downtown area you can look at going to the Brewhouse or Orso's. The more local favorite is Brewhouse. I recommend if you to this place that you call ahead for a reservation or be prepared for a small wait while you look at the art shop next door. Closer to you is Dami if you are in the mood for Sushi or Japanese style food. Not bad prices moderate for Alaska. If you want a bit different there are two of my favorites which are Ginger across from the mall on the 5th Ave side which is asian fusion and a new place that opened up is Crush which is attached to the mall across from the Nordstrom entrance on the 6th Ave side. The have an excellent selection of wine and good beers as well as 2 sizes of plates of various scrumptious morsels. I always get a couple of the small plates and my friends and I get a little from each plate.
One of the main places I cannot stand is Phylisses on 5th Ave. The only time they have business is when there are tourists. I hoe you find a place you enjoy.