The best time to visit Nineveh is spring (March–May) or autumn (October–November), when temperatures in the Mosul region are mild. Summers are brutally hot, with temperatures regularly exceeding 40°C (104°F), making outdoor site visits uncomfortable and potentially dangerous. Winters are cold but manageable.
The more important consideration is security. The Nineveh Governorate, including Mosul, was under ISIS control from June 2014 until late 2016–early 2017. The city has been rebuilding since then, but the situation remains fluid. Check current travel advisories from your government before planning any visit, and make arrangements with a reputable local guide. Independent visits to the archaeological sites without local knowledge are not recommended.