Tonyandkaren’s suggestion isn’t a bad loop. But it’s near a 1,000 mile trip. So if you want to drive 3 days and sight-see 4 days you’ll be driving about 6 or 7 hours on the driving days. And at best you’ll only have a day at each place, not much time for extracurricular activities. You could trim a couple of hundred miles off by going from Zion to Grand Canyon to Sedona and on to Vegas. But I can’t suggest anything shorter and still be able to see any nice country. With a week you’ll just have to settle for a taste of what you see and plan another trip to those places you really like.
As far as roads go you could take I-15 and then route 9 into Zion. And then 89 and 64 to the Canyon. If you go to Sedona you can go back to 89 or take 64 to Williams, then I-40 back to Flagstaff. To Sedona you have two choices, I-17 to route 179, then on to Sedona. Or 89A from Flagstaff to Sedona. The latter is a very pretty drive. But it’s a two lane mountain road with steep grades and tight curves. It’s your call whether you would be comfortable with that. If you have a big RV I-17 is probably the better choice. Good luck and I hope you have an enjoyable trip.
