After we've seen the Grand Canyon is it important to see the others?

No. Waste of time. After an hour at the GC, its time to head for the lounge.

What "others" are you talking about?

Each of the canyons in "canyon country" has its own charm and interest. The best way I've heard it described is like music. Bryce Canyon is like a whimsical, flute quartet. Zion is like an majestic organ concerto. GC is like a full orchestra. Each should be visited in order to appreciate them all.

Canyonlands, I should mention, is like the GC except there are no crowds or facilities (but please don't tell anyone -- I don't want the crowds to discover this place!)

Consider reversing your itinerary to visit the South Rim of the Grand Canyon last if possible.

If you have to ask if it's worth seeing canyons in the southwest other than the Grand Canyon, you probably wouldn't appreciate the distinctions anyway.

Just stay in Vegas and watch a few National Geographic specials on the hotel television if you want to see some "important" natural treasures on your vacation.

There is no question Gr. CAnyon is something to see. Unless you are going to do some hiking, however, you can see the Canyon from every viewing point on the east and west rim (South Rim) in a day or less. A canyon that impressed me more was Bryce Canyon and if you haven't been there do visit. There is one major difference. When viewing Gr. Canyon from the rim everything is so far away. When you visit Bryce you can almost reach out and touch the magnificent rock formations. They are two totally different experiences.