There is some construction going on as the building is refurbished, but all of the museums/ visitor information centers are open
This is up Big Cottonwood Canyon and is a little under 2 miles round trip and fairly gentle uphill on the way ending at the namesake small cave (yes, you can get in the water if you want!). Generally in mid May, this is snow free- though the water is often high as snowmelt season is underway
We've put the all trails up on this. For an extra challenge, do the west face (there are multiple options for approaching the west face while the east face trail can be accessed from Millcreek Canyon). Zach's personal best on the west face is 57 minutes trailhead to summit (uphill only)