Pets are optional. More and more facilities are allowing them because research shows that they greatly increase the quality of life for their owners. Even an Alzheimers unit that I used to visit regularly allowed pets. Ask about this.
Try to find one with “continuum of care,” where you can move from an apartment (full kitchen, total indpendence if wanted) through nursing care in the same facility. It makes a big difference.
Insurance can be tricky. Some insurance policies will only cover skilled nursing care in a designated nursing home, some are more flexible. Talk to your insurance agent/benefits manager. Each facility should also have a staff person who lives to interact with insurance companies. Make friends with this person.
More and more facilities are being built with day care facilities on the premices, and residents are being encouraged to interact with the children (doing crafts together, celebrating birthdays together, etc.) on a regular basis. Again, this is because research shows that both the children and the elders benefit. However, this should be optional if your mother doesn’t like children.
Check the design. Rather than long, straight hallways (hard for seniors with walkers, mobility issues to go a long way) there should be short stretches of hallway and then a jog, or widening with chairs, books, a birdcage (a place to sit and rest and a reason to sit down that isn’t "I’m feeble). As much as possible should be on the main floor. There should be easy access to the outdoors, and the grounds should be easy to navigate. Check for a hairdresser, convenience store, post office on site.
When you visit, see if the staff greet residents by name. Talk to the kitchen help and see how long they have worked there. Ditto the maintenance staff. Visit at several different times of day. Just sit in the main lounge, in other places around the facility for a few hours and see what you observe.
Many places have extra bedrooms built into the facility for visiting family.
That’s all I can think of right now.