Located on the BYU campus, they offer free admission to the general public and hosts a number of family friendly events throughout the year, many of them free or low cost. This museum has over 2 million specimens on display, both preserved and live.
My kids love going to the Bean Museum and seeing the animals. They do live animal shows weekdays at 7:30 pm, which is fun. It's free every day and not crowded. In addition to the exhibits, they have a small slide for younger kids.