Spoiler: April–May or September–October. Beyond that, it depends heavily on which part of Turkey you're visiting.
Best overall: mid-April to mid-June, and mid-September to mid-October. Warm but not baking; everything open; shoulder pricing.
Apr–May and Sep–Oct are perfect. Jul–Aug is crowded and 30°C+. Dec–Feb is cold, grey, and 40% cheaper on hotels — viable if you only care about museums.
Apr–May for wildflowers and pleasant balloon flights. Oct for golden-hour light. Winter balloons fly less often but the snow-dusted fairy chimneys are magical. Jul–Aug is hot (35°C+) but flights still run at dawn.
Swimming from May to October. Peak heat and crowds Jul–Aug; May–Jun and Sep are the sweet spot. Nov–Apr is mild but most beach resorts close.
Only really worth visiting Jun–Sep. Rainy year-round but summer has the green highlands at their best.
Late Dec through early March. Best in Jan–Feb.
Ramadan dates shift each year. Restaurants in tourist areas stay open for non-Muslims; bars may be quieter. The festive iftar meals at sunset are worth planning around if you visit during the month.
Any shoulder-season weekend works. If you're choosing between April and October, April edges out for flowers and green; October for light and slightly warmer seas.
Activate these from home — cheaper and simpler than sorting them at the airport.