Vail Mountain's one gondola is the Eagle Bahn, which is located in Lionshead Village, just steps from Vail Square and the Arrabelle hotel and residences
. Eagle Bahn zooms skiers up the west side of Vail Mountain, to Adventure Ridge and Eagle's Nest (and that area's restaurants), from which a series of mostly intermediate and a few expert trails descend back down the Frontside to the village. Alternatively, from here you can ski from Eagle's Nest to the Game Creek Express Lift and take that to Wildwood (you cannot, however, get from the base of the Game Creek Express Lift back to Eagle's Nest - to get to Eagle's Nest from this area is to ride Game Creek Express Lift to the top, and then ski down the (green) Eagle's Nest Ridge trail.
In addition to this one gondola, some 30 lifts serve Vail Mountain, including 16 high-speed quads.
Here's a trail map of Vail Mountain.