Well, there is still snow in the mountains in Salt Lake, so a lot of the hikes high in the canyons will be iffy.
I might recommend Grandeur Peak which begins at the Church Fork trailhead up Millcreek canyon. It should be easy to look up. There is an west-facing access to this peak that is much more strenuous.
There is also Ferguson canyon in the Olympus cove area but I image that it will be snowed-in up higher so snow shoes may be necessary.
Another popular hike is Mount Olympus. The trailhead is easy to find, even for an out-of-towner. It is popular with locals for convenience. Again, there may be issues with snow and the last part of the hike is a scramble to make things worse.
These are few off the top of my head. Good luck!