I helped a friend trap a few times in the mid 1980's in the upper Chena and we never got a fox. One huge lynx and lots of ermine. The thought was that the fox were not too interested in the cubbies hiding the traps.
As for hunting them and a few coyotes people used to go to the back side of the Fort, but that area is now filled with houses near northpole/badger road. I don't think you can fire a rifle in the Chena flood control area now. Shot guns and archery only. How about the end of Cushman road past the rifle range?
Rosey creek should have some good hunting for most anything small still.
Have you guys gone north on the Steese or haul road yet? It has gotten more developed since the big mines and what not have gone in, but there were several old mining roads that we could walk in on off the haul road and go bird hunting and moose hunting. (SHARP TAILS!) Most of the moose hunting turned into berry picking while glassing the burned areas. Turned out that some guys can't handle large quantities of blue berries. The other guys in the group came across the pile later in the day and thought there was a bear in the area. Too funny.
Back in the day, there was a "main" road taking off to the east from the haul road about 5 miles from Fox. You could drive a 4WD up the ruts to the top of the ridge and park in a big wide spot. A 2WD truck could make it as long as it was dry. Down the back side of the ridge was for ATVs only and even they got stuck in the muck at the bottom. The area had been burned over in the 1940's or 1950's and was full of downed black spruce. (Until you have hauled a moose out of a willow patch that has grown up through a black spruce "pick-up stick" burn area you have not lived the true Alaskan life. Always go moose hunting with a chain saw.) The mining road continued across a bog and then up a ridge for miles and miles to the Steese.
I checked on Google Earth and the area shows up but appears to be getting mined on the southern side of the main ridge.
For scouting you should go up to the Gee Whiz building on the hill and find the LANDSAT image office. They have lots of near infra red photos of the state on file that are free to look at. Look for areas that were burned over in the past 50 to 60 years. There were lots of fires north of town back then. These areas are starting to become mature forest again, but could still offer good habit for hunting. Near infra red is cool because the different vegetation types show up better than with standard color images.