Did you ask what stage of the rut the elk would be in??? Calling is one of the best ways to locate elk. Calling can be used to draw them to your location or just as a locator for a spot and stalk.

As far as trails, ime elk trails look like cattle paths, often beat down to bare dirt. It is always good to check water, streams, rivers, etc for tracks and trails leading to and from. Meadows or hay fields often provide the food source for elk and should always be considered. If you can find a major trail setting up along them can prove to be a good bet, but you may find once on a major trail a spider web effect to other trails may appear and in this case picking a spot may prove a tough task. Now having never hunted elk in Utah this may not be the case. In my area this is what happens 99% of the time once you head off into the timbers, I chose to either hunt the major trail or the source for which the elk are coming to (ie: food or water).

First find out if calling is an option, if so start scouting by bugling or cow calling. Scout thoroughly for food and water sources. Get up high and glass. Spot and stalking is another method that may be available depending on the terrain in the area. Talking with locals, businesses, etc is always a good bet, as is the CO' s. While not all the info is super useful it may help to narrow the scope a little.

Good luck and have fun!!