It's been awhile since you posted this question - I wonder if you have made a move yet? I often have clients looking in both towns and only once have I had someone settle on one town and then want to move to the other. I think the towns are similar - kids sports programs are offered in both (soccer actually overlaps). Bernardsville is a regional school district pulling kids from Peapack-Gladstone, Bedminster and Far Hills. Bernards Township (Basking Ridge) has it's own district.
Both are wonderful areas of Somerset County. If you would like more information on the towns, the town's website offer an abudence of informaiton for all the upcoming events. My website lists all the towns in Somerset County, you are welcome to visit it. http://www.somersetcountyexperts.com
Or call me firstname.lastname@example.org
Both are great areas. The challenge becomes finding property in those towns for $500,00 and below. I ran a search, and the Garden State MLS shows 6 homes in Basking Ridge that fit your criteria and 1 in Bernardsville. Both towns are top notch towns and I think either one would be a great fit for what you describe.
As far as other towns, I would highly recommend Bridgewater. It is a "Blue Ribbon" school system. They have a very active recreation department. There will be a multitude of properties that meet your needs in your price range. I ran a search using .75 of an acre as a minimum and got 47 properties in your range. When I increase the lot size to 1 acre or bigger I still get 21 properties.
Please contact me and I would be happy to help you find your next home. My cell is 908-507-8178 I grew up in Somerset County and still live here today.
My website: http://www.marcpollak.com
I hope this is helpful and look forward to hearing from you so I can share my findings in more detail with you.