As for terrain at Big Sky . . . it's a huge place with a lot of variety at all ability levels. Total skiable acreage is 5800 acres, spread across 7-10 sections depending on how you want to count. Taking a free mountain tour is well worth considering at the beginning of a trip for first-timers. Bill and I did that in 2012. The tour covered several areas in two hours and it was well worth it, even though the skiing was all on blue groomers. They do tours at different levels from green to blue. The "blue blue" groups move pretty fast. Bill did another tour this time one morning. The group had to decide whether to do North or South. North seems to mean Moonlight Basin, while South means more of Andesite Mtn. Tours start at 10:45 and 1:00 near the main base ski school.
For intermediates, starting with Ramcharger 8 up Andesite is a good approach. Taking it easy by checking out a green that leads to the Southern Comfort lift is worth considering for folks not yet adjusted to higher altitude. The blues called Lizette and Pomp (harder) are good fun. Although most of the terrain is 7500-10,000 not too high compared to Colorado. The other side of Andesite has Elk Park Ridge and Elk Park Meadow, plus nice black tree runs that are relatively short. The third section of Andesite has fun blue bump runs like Africa and Congo. In short, it's easy to spend an entire day just on Andesite. Even advanced/expert skiers won't feel bored staying on Ram8 and Thunder Wolf if the upper mountain is socked in or has high wind issues.
The other area that's good for adventurous intermediates or advanced skiers more interested in trees than chutes is over at Moonlight Basin. Takes a little while to ski over (20-30 min) from Mountain Village so better to commit to staying there for a while. The tricky part to Moonlight is that the Madison Base is above the high-speed Six Shooter lift. Can take the Derringer quad up to Madison from the base of Six Shooter but that's a slow beginner lift. At least there is a couple porta-potties at the top of Six Shooter.
@lisamamot showed me Single Jack (black) off Lookout Ridge (blue). Great fun! Bill liked Marshall (black) off Lookout. Horseshoe (blue) is a long, long groomer. Was a bit of an adventure to get across the top off Lone Tree lift because of strong gusts and blowing snow the morning I took some folks that way, but it was worth the effort. The trail was empty, no wind, mostly groomed with 4-5 inches of fresh untracked snow on the sides.
Didn't ski the Bowl right under Lone Peak at all this time. Too much snow, too little visibility after the first day so the Bowl was closed when I made it over there even though Powder Seeker (6-seater bubble lift) was open.
Did make it to Dakota again after the snow started a few days after the little tour by
@Skisailor on Sat afternoon. I was headed that way solo and wasn't sure what I would do when I got there. Met a woman on the slow section of the cat track on the way to the Shedhorn lift. Struck up a conversation. She turned out to be solo as well. Wanted to check out Dakota but had never been there. She was at Big Sky from Colorado for a Wildnerness Medicine conference. We skied together for the next 1.5 hours. I managed to find the same area in the Dakota #1 trees. It was DEEP and a bit heavy. Could have used skis wider than 103 underfoot. But the second run was better. Needed more speed. Definitely lucked out in finding a ski buddy or else I wouldn't have done more than a few turns in the trees before heading right out to Badlands (blue). The snow was boot deep on Badlands, which had been groomed at some point.
My favorite tree run after it started snowing was Shady Chute on Andesite. I skied it when the snow was still light and fluffy. Knee deep in places with very few tracks. Bill and I spent an afternoon checking out most of the blacks off Silver Knife (steep blue) after the first snowy day. Blackfoot (black) is another good one for people starting to explore bumps because it's easy to bail out on either side to a groomer. Can do 4-5 turns or 10-12 before deciding whether or not to go all the way. Colter's Hell is a more open black that's more bumps than glade and a little shorter than Blackfoot.
Silver Knife is the way to get to The Cabin, the restaurant above Lone Mountain Sports.
Turns out the Lobo (blue) off the Swifty (Swift Current) lift has a good view of the front side of Andesite, meaning from Africa (blue) over to Ram8.
Even with an entire week, it's hard to cover much more than a few sections of Big Sky. I can see why some people just keep going back and aren't really that interested in skiing elsewhere.