F.B. Meekins Cooperative Preschool in Vienna. It does rent space from Emmaus Church, but it is not affiliated and it is not in a basement! It is in the education building and has separate classrooms based on age. My 2 year old son is 2 attends and I have been very pleased this year with the school, teachers and staff, the play based approach, and the overall community. Good luck!

Hunter Mill Country Day in Vienna

The Frying Pan Park preschool looks cool, and the kids there always seem to have fun. We didn't go because it was too much of a schlep.

http://fryingpanpark.org/programs-and-classes/katydid-preschool/

Meekins ( I think that is the name.) It's a coop preschool in a church basement.

Parkwood in Vienna is not church affiliated. No first hand experience, but neighbors here have all been happy.

Discovery Woods and Hunter Mill Country Day School.

Don't suppose you would prefer a synagogue...

Here's a play-based preschool with Reggio Emelia leanings:

http://www.bethelhebrew.org/learning/preschool

Western edge of Alexandria

FB Meekins in Vienna is located in a church, but is not church-affliliated. The school rents the space from the church.