West Yellowstone is one half mile from the park gate. We stayed there last summer. It's a nice anchor point to access the park and there are local things to do and decent places to eat. Three miles in and we were seeing bison, bald eagles, and more. We stayed in Colter Bay on the way out (Grand Teton)
This last summer we entered the park there (we live near Portland) and returned home via Jackson Hole, etc. When I do it again, I will go through the Tetons at start, add an extra day or so there to explore more, and still stay in West Yellowstone.
The Tetons offer a nice "warm up" to Yellowstone and have beauty in their own right.
History: '08 View, '05 Chinook, '01 Jamboree 24D, '78 Apache Popup, 81 Komfort Tlr,
84 Mazda B2000 'w canopy,
Tent from wedding shower in '96