Salt Lake City, Utah had its day in the sun when in February, 2002 it hosted the XIX Winter Olympics. The world sat up and noticed the wonderful snow and beautiful weather, while enjoying a cyber tour of all that this fabulous city had to offer. Soon enough folks had no trouble deciding where to go on their next vacation, and the enthusiasm hasn't died down a bit.
Located in north-central Utah, Salt Lake is easily accessible by I-80, I-84 or I-15. There are Welcome Centers at key entry points to give visitors all the information they may need to have a truly nice time. You need to take I-80 if you're driving into Salt Lake from Wyoming or from Nevada. From the northwest area of Idaho you would need to be on I-84.
As for public transport, Greyhound Bus Lines has a stop at Salt Lake besides other neighboring places like Ogden, Provo, and even down to St. George. This makes exploring the local delights a breeze. The Utah Transit Authority has regular services to the ski resorts and Salt Lake Valley. Amtrak has services to Salt Lake, Ogden, and Provo besides the rest of the state. So here's another option for sight seeing.
From the Grand Canyon you would have an 8 hour drive northwards to hit Salt Lake. From the entrance road to the Canyon you need to turn northward, which would be your left, on to AZ-64. Make a left on to US-89. After about 284 miles you'll be at the ramp that takes you to I-70. Another left for a couple of miles brings you to I-15 and you're headed for Salt Lake.