“Amazing area with everything you could want. Chutes, open bowls, gnarly lines and no one else around”
— Colin Tuttle
Start at the Hyalite trailhead and head up for a few miles. Once you're right in between Palace Butte and Maid of the Mist mountain, you'll hit a little field, with a trail branch to the right. Take that and start the terrible part. There will probably be a few skin tracks, but stick left. Right gets real steep and can get 'cliffy'.
Don't go into the drainage and don't get left of the mountain (unless you want to head to that part of the MotM basin). After the real steep trees, you'll come out on to some open faces. With a bit easier climbing in and out of trees, you'll come out into the MotM basin.
There is some amazing mini areas down in the basin, or you can head up to the ridges for bigger stuff. Head up and right towards Swim Lake and there's a real easy ridge access. From there you'll have a mid-sized, but short chute to get into Palace Butte Basin. To exit, you can drop back west right by Alex Lowe peak, then do a quick'ish skin up to the saddle between Elephant and Blackmore. Don't try to take the ridge up to Elephant and then over to Blackmore, unless you've got ropes and some big balls. Or you can just go all the way back the way you came.
It should be mentioned that the Palace Butte basin is a hanging valley, and you shouldn't try to ski straight down to the trailhead. Some people bring ropes and rap out over Twin falls, a popular ice climbing area, and you could probably billygoat it out over around and above some cliffs, but I can't help you with that.