East Vail is on the Denver side of the Golden Peaks part of the mountain...You have the golf course and Ford park in this general area...I haven`t spent much time there as it is mostly residential. Golden Peaks offers a lift with easy terrain and you also would have the option to take the bus on to the Main Village (or ski there after unloading at mid station on chair 6).
West Vail is going towards Beaver Creek/Eagle/Glenwood, etc. and seems to have more commercial activity nearby. It is west of Cascade village (a lift you could take up and connect to chair 2, but no easy blues back to it so one the way home, you would likely catch the bus from Lionshead (or Main Village/Golden Peaks if that is where you ended up)
I would ask the VRBO owners how far it is to the bus stop and/or get an exact address and check it out on google maps. With street view, you could try to verify how long a walk it might be.
Driving to the bus stop might be an option, but good parking near the bus stop will fill up early on Pres weekend, so I wouldn`t count on it. You are much better off to stay near an actual bus stop. This shows the bus routes http://www.vailgov.com/docs/dl_forms/busmap72.PDF
The schedules can be found here http://www.vailgov.com/subpage.asp?page_id=162
Vail is not huge, and parking should be free at the Main lot and Lionshead after about 3 pm, so for dinner you could take your car anywhere without much issue if you don`t want to take the bus.