In parenthesis I've included towns, hamlets, and villages that are generally covered by the district as well as zip codes that you can enter for online real estate searches. Note: My description may not be all inclusive, as some district boundries weave in and out of subdivisions and townships. Some zip codes cover multiple districts.
As a general rule property taxes are lower in Oswego and Madison counties than Onondaga County.
Based on standardized test scores and overall academic performance I would recommend the following in no particular order:
Western Suburbs:
1.) West Genesee (Camillus, Fairmount, parts of Onondaga Hill and Geddes)
Zip Codes: 13031, 13219, 13215
West Genesee School District
2.) Westhill (Onondaga Hill, Westvale)
Zip Codes: 13215, 13219
Westhill School District
3.) Skaneateles
Zip Code: 13152
Skaneateles Central Schools - Home Page
4.) Marcellus (Marcellus, and portions of the towns of Camillus and Onondaga)
Zip Code: 13108, 13215, 13031
Marcellus School District
Northern Suburbs:
1.) Baldwinsville (covers the towns of Lysander, Van Buren, and part of Clay)
Zip Codes: 13027, 13090, 13137
http://www.bville.org/
Eastern Suburbs:
1.) Fayetteville-Manlius (covers parts of Manlius, DeWitt, and Pompey)
Zip Codes: 13066, 13104
FAYETTEVILLE-MANLIUS SCHOOLS
2.) Jamesville-DeWitt (covers parts of Onondaga (Southwood), DeWitt,
Jamesville, LaFayette, Pompey and Manlius)
Zip Codes: 13224, 13214, 13078, 13066
Jamesville - Dewitt School District
3.) Cazenovia (this district is in neighboring Madison County, adjacent to F-M)
Zip Codes: 13104, 13035
Cazenovia CSD Home Page
Hope this helps. Welcome to Syracuse.