The best school zone in East Cobb is the Walton High district, followed closely by both the Pope and Lassiter districts.
In terms of location, think of East Cobb as vertically aligned, with the Walton district farthest south (closest to Atlanta), the Pope district in the middle, and the Lassiter district farthest north in East Cobb (farthest from Atlanta).
The commercial heart of East Cobb is in the Walton district (some spillover into the Pope area), while the Lassiter district is more newly developed. The Walton area is more well established and expensive, whereas the Lassiter area will get you more house for the same money, with the Pope area in between.
Personally, the Lassiter area is kind of far away for my taste, and your budget is high enough for me to recommend the Walton and Pope areas first.
What kind of houses are you looking for? If you want a new house, Walton area can be quite expensive, I think average new home is somewhere around a million. But older homes are easily within your budget.
The newer houses tend to be more cookie-cutter subdivision style houses. The Walton area, especially the southern parts of the district, close to the river, have very nice older neighborhoods with more architectural variety and landscaping. It's more rare in the Pope area, which is more subdivisions...
My advice would be to look around the Walton area, specifically the more southern portions along Columns Drive, Paper Mill Road, Lower Roswell Road, Woodlawn Drive, etc. These are the nicest parts of East Cobb and you should find good homes for your budget.
East Cobb is also home to some of the best schools in the state (and country). Walton High is ranked #103 out of the 27,000 high schools in the US (highest in GA) and Pope and Lassiter are up there too. These are all the top ranked schools in East Cobb, I would advise sticking to these school districts:
Elementary (
map here)
Mount Bethel
Sope Creek
Timber Ridge
East Side
Tritt
Murdock
Mountain View
Shallowford Falls
Garrison Mill
Davis
Rocky Mount
Middle (
map here)
Dodgen
Dickerson
Hightower Trail
Simpson
Mabry
High (
map here)
Walton
Pope
Lassiter
I suggest you take a look at that high school map. You'll notice the high achieving schools are all on the very eastern border. The Sprayberry and Wheeler areas (in between East Cobb and Marietta) are both decent, but not exceptional. The South Cobb areas are flat-out awful. The western areas are decent.