I lived/worked in Yellowstone for a full summer when I was in college. The first thing you need to understand about Yellowstone is that it is HUGE. Really, freakin, huge. West Yellowstone might be an hour from some of the main areas of the park, but it is NOT an hour from the park. You are just minutes from the west entrance as it sits adjacent to it. Keep in mind that even when staying in the park you will still likely be an hour or more from some of the main areas.
For example, if you're staying in Canyon Village, it's over an hour drive to Old Faithful. From WY (west yellowstone), it's about 45 minutes. The Tower/Roosevelt area (which is in my opinion one of the most beautiful area of the park with, at least in my experience, the fewest amount of people) is just as far from the Old Faithful Lodge as it is from WY. Firehole River, which is a great swimming hole with huge rocks to jump from and a natural "waterslide" (ascend up river just a bit to some rapids. Jump in and it will suck you under for a few seconds and then spit you out maybe 20 yards down) is just 30 minutes from WY, but over 90 minutes from Tower/Roosevelt.
All that said, I would say staying in the park is preferable to outside the park. But don't feel like you're missing out if you stay in WY, or you'll be driving significantly more than if you stayed in the park boundaries. Bottom line is no matter where you stay, you're going to be doing a lot of driving if you want to see a lot of different areas. But the scenery is amazing, so the drives are quite enjoyable.