Originally Posted by PNW Judy
Bob's route is a great suggestion. Another possibility is to continue north from Arches through Wyoming to see the Grand Tetons and Yellowstone, then through Montana to see Glacier, then across beautiful northern Idaho to eastern WA. In eastern WA, you can either speed across the state via I-90 and see the coulees. Or you can go along the northern part of the state and see Grand Coulee Dam and cross the Cascades via the North Cascades Hwy. This highway closes for the winter so this route may not work for you depending on when you're traveling this way.
Of course, you could do Grand Canyon/Zion/Bryce and then cross over to California and go up the coast.
Or, if time is a factor, you could take the quckest route and, from Arches, go to Salt Lake City-Boise-Pendleton-Richland-Yakima-Ellensburg-Seattle.