Eight days is barely enough time to cover these places if those included your travel days from your home to Las Vegas and back.
Consider this plan:
Day 2: Grand Canyon AM. Drive to Page AZ PM. 3 hour drive. Overnight
Day 3: Do AM tour of Antelope Canyon. Drive to Monument Valley Tribal Park. 3 hour drive. Do back country tour of Monument Valley in evening. Overnight
Day 5: Drive scenic byway highway 12 to Bryce. 3 hour to most of the day, depending on stops along the way. Overnight.
Day 6: Bryce AM. Drive to Springdale Utah PM. 2.5 hour drive. Overnight
Day 7: Zion NP.
Dag 8: Zion AM. Return to Las Vegas for late afternoon flight home. 3 hour drive. Gain an hour entering Nevada.
Grand Staircase is a vast, remote region that's mostly inaccessibly by regular passenger car. You will see some of it from viewpoints along highway 12.
For lodging, you want to stay at one of the 6 hotels inside the Grand Canyon. If there's no availability there, then look in the nearby town of Tusayan.
For Page, use TA for hotel listings and reviews and then book directly with the hotel.
For Monument Valley, there are two lodging options. The View would be the first choice. Gouldings Lodge would be the second choice.
For Bryce, the first choice would be the lodge inside the park. Otherwise, look at the Best Western Ruby's Inn complex near the park entrance.
For Zion, you want to stay in the town of Springdale, Utah which is literally at the entrance to the park. If you stay in Springdale, you can leave your car at your hotel and use the town shuttle to connect with the mandatory Zion Park shuttle at the visitor center. Stay anywhere else and you will be searching for a parking place in designated lots in Springdale and paying $22 for all day.
If any of the people in your traveling party are 62 or older, he/she should plan on purchasing the Senior Lifetime park pass. It costs $80 and will give the passholder and all passengers in the vehicle entry to all the national parks on your itinerary. If no one is that age, then plan on purchasing an annual pass for $80. It has the same benefits. Without the pass, you'll pay between $30 to $35 per vehicle for each park entrance. The Grand Canyon, Zion and Bryce are $35 a piece.
You need to make your hotel reservations before you purchase airfare. Don't be surprised if you find it a bit of a challenge..Edited: 03 August 2018, 00:07