See here: http://efukikata..com/2015/07/top-101-best-secondary-schools-in.html
In the link above you will see the best secondary schools in Lagos, Rivers State, Abuja, etc. They are really incredible.
Meanwhile view some excerpts here:

Top 101 Best Secondary schools in Nigeria.
Kings’ College, Lagos
Atlantic Hall, Poka-Epe, Lagos
Loyola Jesuit College, Gidan Mangoro, Karu-Karshi Road, Abuja
Grange Schools, Ikeja, Lagos Sate
Christ The King College, Onitsha
Vivian Fowler Memorial College, Chief T. A. Doherty Layout, Oregun, Ikeja in Lagos
Day Waterman College, Ikoyi, Lagos
LEKKI BRITISH INTERNATIONAL SCHOOL Victoria Arobieke Street, off Admiralty Way, Lekki Phase 1, Lagos. Lekki British International School
Lumen Christi International High School, Uromi, Edo State
Corona Secondary School, Agbara, Ogun State