Winter: October to March is hands down the best time to visit Jaipur.
Although this time of the year is classified as winter season, the weather between Oct to Mar is very mild. It is usually bright and sunny during the daytime. You do not need heavy woolen clothes during the daytime as the sun shines bright. The night temperatures do drop to a low of 10 °C, so you would need warm clothes after sunset.
Most popular festivals in the region are also held during this time of the year: Diwali (Oct/Nov), Holi (Feb/March), Jaipur Elephant Festival (March), Kite-flying Festival (Jan), Jaipur Literature Festival (Jan). If you are travelling in these months, make sure your time in Jaipur coincides with these festivals, so you can enjoy the full local cultural experience.
Summer: April and May is the peak summer season when temperatures go well past 100 °F (38°-40°C). While it is generally off-season for cultural and historical tourism.
The upside is that the hotels drop down their prices by up to 50% during the summer months. So, if you are tight on the budget, braving the heat is worth it.
Monsoon: The monsoon rains hit the region in June, and the spells last until September. The rains cool the temperatures down. This is generally considered the shoulder season. A good time to visit Jaipur and find affordable accommodation if occasional showers won’t trouble you