The temple grounds are well-maintained and open to the public. There are paths, gardens, and benches, and the building itself is best seen in the late afternoon when the light comes from the west and hits the facade directly. It is not a large temple by LDS standards, but it sits beautifully in its setting, with the Teton Range visible to the east on clear days.
Non-members who want to understand what LDS temples are and why they matter to the community will find the grounds a good place to observe — staff and members are generally friendly and willing to talk. Don't expect a tour of the interior; that's genuinely not on offer. But if you are curious about LDS culture and architecture, and you're already in Rexburg, the temple is an easy fifteen-minute stop from the town centre.