Affordability vs. Desirability

Hi! We ware wanting to move to the I5 corridor of WA. We want to purchase a house but that reality seems to be heading beyond our grasp. We could buy in Olympia/Lacey but I don't get the best of vibes there. I hear mostly negative things to be honest. Also, thinking maybe Gig Harbor would be a good place to land. We had a terrible experience in Portland, OR so we don't want to live in the Portland Metro area (i.e Vancouver, WA or Camas). Snohomish is another possible option but we know nothing about it other than it's more rural.

We do require good private education and proximity to fun family activities. I work remotely but kind of need to be in driving distance of Seattle.

A part of me wonders if we should just rent where we ultimately want to be like West Seattle or East Side suburb and forget about purchasing for now.

Any help would be greatly appreciated!

TC 250k, Budget 4k a month for rent or mortgage is the most I want to pay.