Noonday means happening at noon, or belonging to that time of day when the sun is highest. You meet it most in the phrase the noonday sun — the hard, bright light in the middle of the day — and in older or story-like writing. Everyday English now says noon, midday, or twelve o’clock. Though actually, noonday is not a different time from noon; it is the same hour in an older coat. A student writing to a friend would sound a bit grand saying “Let’s meet at noonday.”