S.-
My daughter attends preschool at North Canyon Preschool. It is in North Phoenix but I don't know have the same type of thing in Mesa. But, it is a preschool that is located at a high school. It is similar to a private preschool. They have a director and an assistant director. It is $300 for the year. They go for about 3 hrs a day Tues. Weds. and Thurs. from Sept-Dec then from Jan-May. The "catch" is that the high school students observe the preschool kids for there child development classes. I was a little concerned at first but, my daughter went last year and love it. It was a very positive experience and we will be attending next year too. The director and her assistant are great. They take take potty trained 3 year olds by Sept 1. They may take your 2 yr old since she is almost 3.
Also I sign my girls up for activities through the city. They have dance, tumbling, swimming, art and crafts etc. They are all very reasonably priced.
In the pass through the City of Phoenix (I am sure they have it in Mesa too) I have put my daughter in a class that is like a preschool setting where they learn basic letters and numbers.
Good Luck finding something in your area
Take Care
