From your VRBO description, I take it you will be driving up the north side of the Mesa. Can't recall the mileage, but its probably most of ten miles to the top, 11 to the Mesa Top parking lot and 14 or 15 to the Visitor Center parking lot. Grand Mesa Lodge is between the Visitor Center parkingand the Mesa Top parking.
Go into Mesa Top in the easterly entrance--its a one way loop. Nice big area, unheated pit toilets and changing rooms, never seen it crowded. Easy access to the west part of Mesa, Lands End. Can get to the Cottonwoods to the north. Watch the closed and xc skier areas if you cross the highway toward Cottonwoods. The only legal area north of highway in that area is on the trail to the cottonwoods. South and west from Mesa Top is open riding.
Visitor Center can get kind of crowded but it is the way to the whole rest of the Mesa, to the east and south.
There is a trail between these two lots across Island Reservoir that comes close Grand Mesa Lodge.
Get a map. You will need it. Start with the State association website , snowmobilecolo.com. Not sure of where to get hard copies. Check with the businesses up there-- Grand Mesa Lodge, Thunder Mountain, and Alexander Lodge.