I teach seventh grade, so I'm not 100% sure what you might want to look for in a kindergarten program.
My suggestion for ideal student-teacher ratio would be fewer than 20 per teacher. 15 would be ideal.
Accreditation wise - I'm guessing this goes state by state but here in NY it would be an early childhood specialist. I'm sure there are further degrees licensing one could get, but basically you want to make sure your child's teacher is licensed in teaching kindergarten. I, personally, would also be curious about how the teacher had been teaching kindergarten. 5 years in I feel like I know seventh grade like the back of my hand! Someone switching grades or with no experience would make me slightly concerned.
An overview of the curriculum for the year would be good to hear - it shows they're thinking ahead about what they're going to do, not going minute by minute. NJ adopted and uses the Common Core Standards, so here is a link to what those standards are:
http://commoncore.org/maps/index.php/maps/grades/kindergarten/ That should give you a general idea of what the year would look like. Schools will likely deviate somewhat from that, but not tons.
I'd be curious to hear about their literacy/linguistics programs and how they plan to get/keep kids reading. I'd also want to hear about writing and where their expectations for students are. Kindergarten is all about building reading and writing foundations.
Assessments might also be something you ask about - how are the kids going to be assessed, what are they going to be assessed for? I imagine it's not as rigorous in kindergarten, but I'm guessing kids will be tested at least a few times. I would want to know what they would be assessed on and when.
Those are just a few thoughts from me! Hope that helps!