The one that Lisa C. mentioned at St. John's church is called "New Horizons" on O'Malley road. My son went there for a year, and we liked it just fine. You'd better call them this week, though - they fill up very quickly, but if you call early you may be able to get your choice of morning or afternoon session (we got stuck with the afternoon). Though it's in the church building, it is NOT a religious program, if that's a concern for you (it was for me).
I understand your frustration - I too was surprised to learn that a lot of the "preschool" programs up here are part of larger daycare centers. Oh, the joys of living in Alaska.
Good luck!