Do NOT go there.
The real place in NOT as good as it in photo, because there are some lab work to enhance the color.
This is Indian reservation, they charge $17 (at that time) per cave, with is very expensive. Plus, they only let you stay in that cave for one hour.
Do NOT be fooled by the pic.
If you still want to go, airlines fly to Page AZ (AmericaWest). Rainbow bridge is there, too. It is one of the 7 nature wonders, can be seen by boat ($60).