Ask the director of the child care center if their facility is has NAEYC accreditation.
The National Association for the Education of Young Children has set criteria for sound educational practices for preschool children. They check early childhood education programs who apply before granting them accreditation.
Ask to look around the classrooms at the child care center so you can check out the environment.
Ask what is served for snack.
If the child care center director says "juice," ask what kind. At the preschool where I worked, "juice" was actually powdered drink mix. Choose early childhood education programs that promote health and nutrition for children.
Ask what time, and for how long nap time is.
Some early childhood education program facilities have a set time, and others are more flexible to the parent's wishes. Be aware of this if your current nap schedule is working well for your child, and decide if the child care center director changing it would help or create a problem.
Ask to meet your child's preschool teacher, and then ask her about her class.
Be general; don't grill the preschool teacher. Let her do the talking. This way you get to see how warm and enthusiastic (or not) she is when talking about her preschool class. For preschool children that's one of the most important qualities in a teacher that will make a difference, not, "What skills do your early childhood education programs emphasize for children aged 2.9?" Those are questions you can ask the director, who is the instructional leader of the child care center who sets the curriculum.
Ask to see the curriculum.
Some early childhood education programs have "themes." It can be fun for you to extend your child's learning at home. For example, if there is a "safari week," you might bring your child to the zoo the weekend before. The more experiences your child has early on during his or her preschool years, the more connections to future learning he or she can make!