If you are looking for the homes in the Palm Beach Central High School you will not find a single family to meet your needs. Another great high School is Wellington High. It is in the town of Wellington and is an "A" rated school. Unfortunately, the price range you mention is so competitive that when a property does come to the market it has several offers the day it hits the market.
No matter where you are looking you will need to have your funds in place. Either cash or with a pre-approval from a reputable local mortgage broker or bank. (not their internet based site). If you would like to have an appointment with a lender please call and I will give you several that can help. Good Luck, Ashley