Also, the commuter trains on the New Haven (Connecticut) line are not as well-kept as the ones in Westchester--some issue with part of the funding for their maintenance having to come from the state of CT, which has not wanted to pay it. The trains on that line tend to have more breakdowns, problems like no heat in the winter and no A/C in the summer, more cleanliness issues, etc. The Harlem and Hudson lines in Westchester have been better-maintained and are getting brand-new train cars (which some people actually don't like, as the seats are narrower, etc., but at least they are new and don't break down as often in the snow!)
Westchester generally has very good schools except for a few districts like the ones I mentioned. I think people with kids move here for the schools and then put up with the inconveniences like commuting and parking because the quality of the education is worth it to them. You may be able to find a house near a bus line, as we did, or within walking/biking distance to the train station. Some people also carpool down to the station, or get rides from their spouses
Some stations do have absolutely massive parking lots, like Croton-on-Hudson, but that's more than 30 minutes from Manhattan--about 45 minutes, I think. And there may even be waiting lists for that lot! We used to live in Peekskill, and parking at that station was available and less expensive, but the commute is long (60 minutes) and the schools are problematic.
Good luck!
Karen