I owned my own center and have worked in child care many years.
In my opinion what I want to see when I go into the toddler room is order. Toys in play area, cots stacked nicely, tables set lower for the little ones to be able to sit comfortably, the kids art work on the walls because the teachers think it's beautiful, cubbies that the kids can reach and put their own coats and stuff in them, and the changing table having shelves or someplace for the kids diaper bags so the teacher doesn't have to reach to another place and leave the kiddos on the pad alone. I had individual cubbies that a few diapers and their wipes would fit in.
I also had a mirror on the bottom of those cubbies so the kids could see themselves while laying down, I also had some toys attached to the wall so they could do stuff. This keeps the kiddo busy and they lay stiller.
The toddler room is a new adventure for kids just coming out of the baby room. The infant room has baby beds, floor padding so they can do tummy time and other infant things.
In the toddler room they lay on cots to nap at certain times of the day and they don't get to lay down other times. They have a full and busy schedule all day and they can't stray too far from that. If the state comes in and sees a kiddo laying down asleep but it's story time or recess time and the whole class is inside because one child is asleep they can lose their license. So in the toddler room the kids lay down for 1 nap per day after lunch. The rest of the day is BUSY!!
You want a parent center so you can see what's going on, what the last inspection shows, if there is any illnesses going round that you should be watchful for, and more.
You want to see security. I will tell you though that if you're divorced the child's father has just as much right to that child as you do. The center cannot keep a child from the parent for any reason. What they "can" do is keep the parent busy doing something while someone else calls 9-1-1 if there is legal cause such as a restraining order or alcohol smell emanating from said parent.
A child care center should fell like they are a surrogate mom for you. If you don't fell right try to ponder and find out what is effecting you.