Rexburg's greatest asset is its location. Yellowstone National Park is roughly 90 miles to the northeast — about an hour and a half's drive via US-20 through West Yellowstone, Montana. Grand Teton National Park is about an hour to the southeast via the Teton Scenic Byway (Highway 33), passing through Driggs and Victor in the Teton Valley. Both parks are genuinely world-class, and Rexburg is a practical and affordable base for visiting either.
The Teton Scenic Byway itself is worth driving for its own sake — the views of the Teton Range from the Idaho side are less visited and, some would argue, more dramatic than those from the Wyoming side. Island Park, to the north on US-20, is a good stop for trout fishing and has access to the western reaches of the Yellowstone ecosystem. If you are spending more than a night in the area, a day at Grand Teton and a day at Yellowstone is the obvious plan — Rexburg puts you in reasonable striking distance of both.