It depends on you .. every season i.e summer, winter have their own merits and demerits.There are things that can only be enjoyed in summer and vice versa. So, you have to decide the best time that suits you.
Winters are from October to March and are the best time to enjoy holidays in Jaipur city. The days are very pleasant but the nights are cold with less than 4°C . Carry heavy woollens while travelling. You can enjoy the sightseeing at the historic forts along with the Elephant Festival in March, Kite Festival during Makar Sankranti and Jaipur Literature Fest in January.
Winters would be the best time to visit Jaipur, as the weather will be good and you would be able to explore the places and enjoy the heritage that the city has to offer
October onwards. I visited Jaipur in last week of Oct'18.
Pretty cool weather even during day time, nights were too cold.
PS: Do carry warm cloths.
December to January- tourists points will be crowed.
Acc. to me Best time is Oct - Nov. based on weather, crowd.