Best time/way/town to buy a house?

Hi! We are a family of four, looking to move to Westchester sometime between summer 2026 and summer 2027. We want good public schools, and an easy-ish commute to the city, so we’ve narrowed our search to Dobbs Ferry, Irvington, Ardsley, Scarsdale and Eastchester. I have a bunch of questions and would appreciate advice!

1) Can any realtors out there let me know if the home inventory is drastically different than what’s available on Zillow, Redfin, etc? We bought our current home after searching on Zillow, and I see no need to pay a realtor unless there are many more homes on the MLS listings than on the public sites.

2) Is there a good time of year to buy a home in Westchester? Since we have a bit of flexibility on timing…

3) Should we consider any additional neighborhoods?

4) We have two kids. Is there anything in particular we should consider re. the timing of the move? Is there something particular to Westchester public schools that would make summer preferable to mid-school year, or vice versa?

We would like to make the transition as smooth as possible for our kids (and our finances, ha), so any and all advice is appreciated! Thank you!