OP, you sound exactly like me! I lived in Berkeley and have also lived in Northborough right outside Boston. To me, the closest place that I've seen in Westchester to strike a great balance between affordable, safe, and also "coming up" is White Plains or Port Chester. I really enjoyed my time living in the WP and found it had a good amount of nature, shopping, dining, young people, diversity, etc. I lived in downtown and worked in NYC so also mostly got around by foot and public transit. I hate driving so this was a huge draw for me.
I also love the "classic Westchester" areas like Rye or Mt. Kisco but they are more established and sleepy than what you're looking for it seems like. They're also more expensive, but since you're coming from the Bay Area I won't make any assumptions on what "expensive" means to you.
You may also want to try looking into CT. It's not unusual for people to live in CT and work in NYC or Westchester - the property taxes are a lot lower. I heard a decent amount of people at IBM live in Ridgefield, which is a GREAT town, but may be too sleepy for you.