jackal

In Anchorage and Fairbanks, there is plenty (even avoiding chain fast food) to eat for under/around $10 per meal--the filling daily special at Taco King, for example, is $8.95 or so (including soda), and most places will have burgers or other similar-sized entrees for ~$8-9 (maybe up to $12 if you get a fancified burger/sandwich with brie and caramelized onions and sauteed mushrooms, etc.); add a couple bucks if you want a soda. Outside of the bigger cities, it's not quite as easy, but most roadhouses will have burgers and sandwiches for probably $15 total (with a soda and tip). If you're going between Denali and Fairbanks, stop at the Monderosa Bar just north of Nenana--probably the best burger in the state.

Anchorage (and even Fairbanks) has some world-class cuisine, though, and if you have a few extra dollars, it's definitely worth splurging on a meal or two. Check out Simon and Seafort's, Orso, Glacier BrewHouse, Kincaid Grill, Jens (not sure if the restaurant is still open after he passed away last year), Southside Bistro, Moose's Tooth, and Bear Tooth. Even a good meal at most of those won't set you back more than $30 (maybe $50 with drinks and tip at Simon's or Orso). Alaska is a bit expensive but not insanely so. (I lived there for 17 years until early last year.)

Following is a list of all of the restaurants I'd say are worth noting in ANC. Some are pricier than others, and some are destination restaurants worth going out of your way (and budget) for, and others are just good deals with good food I used to eat at a lot when I lived there, but if you happen to drive by one of these restaurants and feel like stopping, you know you won't be getting a bad meal.

Simon and Seafort's
Orso
Glacier Brewhouse
Sacks
Club Paris
Moose's Tooth
Bear Tooth
Jens' (if still open)
Southside Bistro
Suite 100
Arctic Roadrunner (usually wins the best burger award in the ANC press)
Tommy's Burger Stop (superior burgers to Arctic Roadrunner, IMHO)
Taco King/Burrito King (good and relatively cheap. I probably ate here three times a week.)
Burrito Factory (inside a gas station but incredible to-go burritos)
Cafe Amsterdam (continental European)
Cafe Croissant (affordable French)
Momma O's (for halibut fish and chips)
Double Musky (45m south of town in Girdwood)
Midnight Sun Brewing tasting room (the food is every bit as good as the beers)
Capri Pizza (run by a Pakistani couple, so get something with South Asian spices or the chicken "fajita" sandwich--yum!)
Spenard Roadhouse (mmm...bacon jam burger and a HUGE bourbon selection!)
Johnny Chicago's (a spot-on copy of Portillo's Italian beef sandwich [mmmm] in Chicago at a slightly higher price)
Lucky Wishbone (straight outta the '50s with very good pan-fried chicken and good burgers)