Hi M.,
I wish you were in our neighborhood here on the east side...I have a lovely little preschool over here! But I digress...
when I was working as a nanny, I observed several childcare arrangements. One most-common one was for the parent to drop off their child at preschool and then a nanny would be employed to pick the child up from preschool; the child would then spend the afternoon in the nanny's care.
I don't have recommendations for preschools in your neck of the woods (although I do like Montessori schools quite a bit, and Cedarwood Waldorf comes highly recommended) , but I do have a suggestion--look at your childcare costs side by side. It may be that you will pay less for the extra hours at a full-day preschool than you might pay combining a half-day program with private aftercare. Individual care is generally more expensive for parents, so if the school has the facility for your son to have some down time (which it should) , AND it is a quality environment (educated teachers, a sense of busy calm about the place, lower teacher turnover and happy-sounding kids), a full day option might be the better consideration. This too depends on how much school your son can tolerate at his age.
Metro ChildCare Resource and Referral is one option I would recommend. This is for Multnomah County, but if you call them, they can give you the number for Washington County. The CCR&R gives parents a list of names of childcare/preschool providers in their immediate area to get them started. If you get through the first list, they give you more names. You can message me if you need help getting phone numbers as I have plenty of info from them in my files.
One more thing-many preschools enroll in January/late winter for autumn enrollment, so if you really like a program, understand that they may be full but might be able to put you on a wait list if any pre-enrolled families drop out or move away. This earlier-than-expected enrollment is often an unwelcome surprise to parents doing this the first time.
Best wishes.