Ideas for you.
1) Write a health-care record management system for Nigerians. A free service that allows doctors to store medical records and notes about patient history and prescriptions. Since most people don't have government IDs, device a way to uniquely identify each person (parents name, place of birth, first name, gender, approximate year of birth, last place where a doctor has accessed the medical record, etc.)
I want to do something like that for Somalia, my home country, but don't have the safety to go back there and deploy it. Might go to the refugee camps in Kenya. Shot an email to Save The Children, no reply yet. I want to make a $100 Android tablet that photographs handwritten prescriptions and stores in a central location. The camera can also function as a way to capture visible problems for remote diagnosis.
If you can just pry data health data from the hands of government and NGOs and put it "out there", you wont be short of help.
2) Start a website where people can submit study materials suitable for cheap printing. Exercises and practice games that can be succinctly printed into a few, multicolumn pages. Get the feds to give you a printing service and churn out study materials, send on donkey backs to villages.
You can advance education tremendously by teaching teachers new games and teaching practices, that are fun for both them and students. Tap into new research on learning, and do the simplest stuff first.
3) Chronicle and catalog a verbal recording of the myriad of languges and dialects in nigeria. Send a voice recorder with several hours and let the elders speak about everything. Transcribe that into IPA and save it for the kids. The cities are growing and languages are dying. Also, provide corpora of your languages free online to linguists and programmers can develop NLP tools. As long as African languages remain oral we wont have a mention in computing.
4) Create an online talent website. Reward people for discovering street musicians, painters, folk artists and inventors. The talent gets a mention, and whoever discovered them gets a prop. Put in some game mechanics to encourage the more affluent people with the technical means to go out of their way to interact with, the often poor, local talents. Ignore government aid and other BS. You can bootstrap this with funds from local businesses and transnationals that want to feel-good aspect of this local involvement.