I am not a real-estate agent, so I can freely give you some insight from someone
born in one of the towns you cite, and very familiar with the others.
In order of (very arguable) generally accepted common belief, here is my breakdown:
Rye (Best of your choices, and I am not from Rye. But a starter home is $1M + at least through this last year's worth of Wall Street Bonuses)
Irvington (Excellent - nice, safe, small River town...)
Mammaroneck (Very Very Good)
Edgemont (Very Good, but my personal belief is that Edgemont is surrounded by too many bad influences
Growing up in Westchester, the Edgemont teens always had easy access to drugs, etc)
Tarrytown (Good, and getting better, but still considered segmented by slow (ESL) and Fast-trackers.
Taxes generally disproportionate to value