Many have baby-sitting for moms. As seniors, the baby-sitting feature probably isn't high priority. Anyway, it's all good. One of my daughters happens to be one, and I've watched some others where I workout. I'm sure are better than others.
Most health clubs make referrals.
Ask if any work particularly well with seniors. If you have a chronic health problem or are recovering from an injury, a competent trainer can be invaluable. So ask questions and educate yourself enough to judge the answers. As one who likes quarterbacking his own situations, knowing how to train my own body appeals to me. I like doing my own research.