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I would take White Plains over Stamford in a heartbeat. I actually live in WP and commute to Greenwich, it is a dream. It's usually a shade under 20 minutes at rush hour. Off hours, I've made it in under 15. I also commuted from WP to Grand Central for 6 years - and I always say it's the best suburb commute. At rush hour, express trains come every 5-10 min. Off hours, there are 2-3 trains per hour. The train tickets are also cheaper from WP than Stamford.
From WP you are central to almost anywhere you may need to go - LI, NJ, Manhattan, etc. I think the schools are also better in WP than Stamford. The one area Stamford and CT will win is taxes. WP is relatively low for Westchester, but the taxes in CT are much lower.
For your price range, you could buy something in those other towns, but you are paying then mostly for (perceived) superiority of schools, and will end up with a much smaller house and property for your money. The taxes in Hastings, Dobbs Ferry, etc are also off the charts.