Abbie, I grew up in Utah and return most summers.
If you want grayling, I can recommend strenuous hike-into spots that would be pretty much guarantees. But that sounds like more of a time commitment than you can make.
I think you'd have no trouble finding fish--couldn't guarantee a grayling, though, but you're at least in water that has them.
If you are willing to spend a long day with maybe a 4-hour hike in then out, I can get you into grayling.
Another option is the fishing in the Uinta Mountains picking one of dozens of lakes around the Mirror Lake Highway. I sent someone else on the board there--he drove to Mirror Lake, found plenty of fish and lots of people. Drive-to lakes with grayling include Trial Lake and Washington Lake. Both of these lakes also have trout.
In those mountain lakes, grayling generally cruise fairly near the shore line. A size 16 or, better yet, 18 dark dry fly placed in their path is generally poetry.