For one of the best all-around views of Vail Mountain, take Mountaintop Express Lift or Northwoods Express Lift up the Frontside (easily reached from either the Vail Village or Golden Peak areas). At the top, you'll be at Vail Mountain's highest elevation (11,250 feet), and the mountain's Patrol Headquarters/Buffalo's area. From here you can take mostly green and blue trails down the Frontside, or blue and black trails down into the Back Bowls, for access to the more secluded (and beautiful) Blue Sky Basin. The photo here is looking east from the Patrol Headquarters area across Headwall Ridge, with the Sleepytime intermediate trail curving off to the right into the Back Bowls.
If you're an intermediate skier looking to get away from the crowds as quickly as possible and seek out some wonderfully scenic and remote terrain, get yourself up to this point (marked "Buffalo's") on the trail map, and then work your way down the Back Bowl's serpentine Sleepytime run, traversing at the base over to Skyline Express Lift. This whisks you up to Belle's Camp, one of the two main peaks at Blue Sky Basin (the other being the top of Pete's Express Lift - this is actually the highest elevation in all of Vail's ski terrain, at 11,570 feet).
Here's a trail map of Vail Mountain.