Buckhead is a HUGE community. The area accounts for 20% of Atlanta city limits land wise according to Buckhead.net, the community website. I suggest you take a look at the website too. In the neighborhoods section they break down the various areas and show home styles along with providing history and different neighborhood attractions.
The Atlanta Interational School is located in the Garden Hills neighborhood in Central Buckhead. It's older than the rest of Buckhead and the homes are small bungalowes instead of Buckhead mega-mansions. But, there are a ton of families in the area, there is alot of diversity with all kinds of races, and the homes are cheap by Buckhead standards. Homes range from the low 400s for fixer uppers to the 700s.
North Buckhead is VERY family oriented. Streets in the area include Old Ivy, Peachtree Dunwoody Rd(within the limits of Buckhead), Wieuca Rd. and Roxboro Road. The homes are nice and vary in styles. You wouldn't be apart of the cookie cutter epidemic in Atlanta, that's for sure.

The neighborhood association is very active and maintains the community's identity. There are also tons of neighborhood sponsored events which take place throughout the year. The link to that neighborhood's website is in the North Buckhead section on Buckhead.net. Living there would also provide priceless convenience to the Lenox Mall/Phipps Plaza area and would put you with in five to ten minutes of Buckhead's most superior restuarants. The homes range from the low 600s to about 1.5 million dollars. While the homes in North Buckhead are pricey by GA standards, you don't feel like there's a sense of snobery found in neighborhoods west of Peachtree and north of West Wesley.
If you are looking for something more exclusive, then that area west of Peachtree and north of West Wesley would certainly fit the bill. Neighbohoods include Hanyes Manor, Tuxedo Park, and Mt. Paran/Northside. It would be quite the task to find homes in these areas under a million dollars. And when you do they will either be teardowns or like 2500 sq. ft. ranches in need of renovations for like $900,000. Most homes are now ranging in the 2-3 million dollar range and can go up to like ten million. It's the most prestigeous part of Atlanta to live in. IMHO, they tend to be more pretentious than other upscale parts of Buckhead. Tuxedo Park and Haynes Manor is the center of Atlanta's old money. Alot of the kids who live along West Paces go to Pace Academy, it's like a country club for the kids of Atlanta's old guard. The rest in other neighborhoods in W. Buckhead attend The Westminster Schools, The Lovett School, the Galloway School, and of course AIS. While these communities are wealthy, they aren't really family oriented. There are very few sidewalks and the yards have shruberry lining the roads as if to insinuate that walking in the neighborhood is frowned upon.
Chastain Park is the popular park of choice for Buckhead parents. There are soooo many people there on the weekends! I have always gotten the sense that it's so packed because the parents don't want their kids playig at home ruining they perfectly manicaured lawns.

I guess which section of Buckhead you move to will be determined by what you want out of a neighborhood. Buckhead is large enough to accomodate whatever you are looking for.