Use the noun modernity when you're talking about the newness of something, like the modernity of the new, sleek skyscraper in your city.
When something is contemporary — it feels like it belongs in the present day — you might take note of its modernity. Sometimes people use the word to discuss something old that's becoming more modern, or attempting to find its place today. You could talk about the balance between tradition and modernity in the Hindu faith, for example. The root of modernity is the Latin word modernus, "modern."