I'm not feeling all that great this morning, so I really hope this makes sense.
In Aberdeen, unless you are catholic or your child has significant additional support needs, each house or property is in the catchment area/zone for ONE primary school. Especially for the City Centre and West End schools you are very unlikely to get your child into an out of zone primary.
So, for example, if you live at no 1 Brown Street your house is zoned for School 1 and that is the school they will attend. While if you lived at no 1 Smith Street your house would be zoned for School 2 and that is the school your child would attend.
You can make a placing request to a primary school that your house is not zoned for, but I wouldn't put all your hopes on it being accepted, especially if it is a desirable school.
The catchment areas apply similarly for secondary schools, but placing requests are probably even less likely.
The most desirable Council secondary schools in Aberdeen are probably:
Cults Academy
Aberdeen Grammar School (which is not a grammar school with an entrance test, the name is historical)
The most desirable council primary schools, in alphabetical order, would be:
Airyhall (new build, West end)
Ashley Road (West End, victorian)
Broomhill (West End)
Cults
Ferryhill
Mile End (new build, West End, probably the 'best' along with Cults)
Milltimber
(this list is not exhaustive. There are over 60 primaries in Aberdeen and I'm mainly working from memory)
There are also three private schools which you don't need to be zoned for:
Robert Gordon's College (has a pretty selective entrance test)
St Margarets School for Girls
Albyn School
You can find details of school inspections by Education Scotland the schools inspection service at www.educationscotland.gov.uk/inspectionandreview/reports/school/index.asp
If you are practicing Catholic, you will also have the option to send your child to one of the city's three catholic primary schools. There is zoning for these, but I'm not entirely clear how the zoning works. They are:
St Peter's RC School
Holy Family RC School
St Joseph's RC School