The gates are open from 7am to 7pm. There is a visitors center outside the park and just inside the park gates. The busiest time is 930isham to 1pm usually. Early is always better as once the suns comes out and it warms up everybody goes out to hike. Purchase your shuttle pass as soon as you can if you want to venture up towards the Lodge and the narrows. You can also hire a private shuttle service in town to take you up to the narrows. Most do not stop at the Lodge. Basically just a ride in and out. Enjoy the canyon!!!
Definitely buy your shuttle passes in advance. My family was at Zion last week and we almost didn't get tickets since they were all sold out. We had to buy the day-before release of tickets the morning before, but that's not a sure thing since they sell out quickly.
I just drove up and got my pass.
We arrived at gate at 1 pm, but we had a national parks season pass which can be acquired online
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