Hi H., welcome to Meridian! I've got a couple of recommendations for you - I've got a 3-year old in preschool and I've got friends with kids as well, so between all of us, we've done a lot of research.
My first recommendation is Challenger School near Chinden and Linder. That's where my son goes and we absolutely love it. It's a private school and the preschool is run like a school instead of a daycare. My son is doing so well and we're just amazed at all of the stuff he learns. It is a little expensive but so worth it. And all kids must be potty trained - no exceptions. They teach the kids to be completely independent.
My second recommendation is Dreamland near the corner of Eagle and Fairview. My son only does Challenger MWF, so we needed to do just one more day a week and he has a lot of fun there too. My 15-month old daughter also attends two days a week and just loves it there. All of the teachers, assistants, and even the director have been there for years and they have a very low turnover rate. Their rates are very reasonable too.
I looked around at a lot of places and asked a lot of people and this was what worked best for us. You can ask for Karen at Challenger or Erica at Dreamland and either can help and answer any questions for you. Good luck!