Boca Raton is an outstanding family oriented community with family friendly neighborhoods, a top ranking school system with plenty of family based amenities from public parks (9 of them), local beaches, museums (Art, Children's and Science to name a few) and a number of other interests for all ages.
Boca Raton is unique in that there isn't really a bad part of town (maybe but for one small section north of downtown called Pearl City), but families tend to gravitate to the west part of the city (whereas Downtown Boca is where the young professionals live and North Boca caters more to students and the universities).
It's obvious from your post that you don't have a great deal of time built into your relocation, I would strongly suggest you work with a local real estate agent (their services to you and other tenants are free) so that he or she can begin to identify suitable housing options and to personally assist in expediting the qualification process while you are still in CA or traveling across country.
The majority of the things that a landlord or property manager looks at (things like credit report, background history, income and employment verification, etc) can be done in advance of you arriving and shared with them to expedite the review process.
I too would be pleased to assist you and your family with your relocation, please feel free to call on me if you need further assistance.
Please contact me at your earliest continence.
Signature International Real Estate LLC