Annadale falls under New York City's Community School District 31, which covers all of Staten Island, and the South Shore is one of the strongest school clusters in the borough.
Local elementary and intermediate options include P.S. 36 and I.S. 75, with other District 31 schools nearby, and the large zoned public high school for the area is Tottenville High School. Annadale also sits near one of the Island's most prominent Catholic high schools, St. Joseph by-the-Sea, which draws South Shore families in numbers.
Families chasing a specialized seat also look to Staten Island Technical High School in New Dorp, one of the city's exam high schools, ranked among the top public high schools in the country by Niche and U.S. News. Admission there is by the citywide SHSAT, not by address.
I don't grade schools for you, that's your call and your family's. What I'll do is point you to the zoned schools for any specific address and the current third-party ratings on Niche, GreatSchools, and U.S. News, so you're deciding on real data.