John and Debbie,
Yes, it is about 20 miles to the West Entrance from Red Rock, but a very pleasant drive.
There are some beautiful places to visit other than Yellowstone. Just ask the people who work at Red Rock. One that I will mention is "Johnny Sack's Cabin." Don't miss it, just south of Island Park.
We were fortunate in that a youth rodeo was going on just down the road (less than a mile past the campground) from Red Rock while we were there. Maybe it goes on all summer.
There are some photos of the cabin area and the rodeo on this web site:
http://dwilliamson.com/Yellowstone/Page.html
Hope you have a great visit.