You are in a "no shoot zone" unfortunately. Layton is right in the middle of mass civilization (at least as mass as it gets for Utah!) and there aren't many places to shoot until you get out away from town a bit.
In Utah, all you have to do is find BLM land, state land, national forest, or some shooter friendly private property and you're good to have fun.
Try around the north end of the Great Salt Lake or up one of the many canyons east of your location. Just make sure there are no permanent structures within 200 yards of you and that there are no fences and you should be fine.
Utah also has some great long range hunting opportunities in just about every unit and for every species. Cross canyon sightings of big bucks,bulls,rams, and vermin make for challenging hunting. Utah also has a massive amount of mule deer hunters during the regular season. It sometimes looks like a pumpkin patch out there so it becomes advantageous for the hunter to learn to shoot long range and you immediately gain a gigantic edge over 99% of the population which might just put a big muley on your wall!
Good shooting and good luck!
If it's not far, it's boring.