Hi Shraddha,
I have been in Jaipur for almost two years and trust me if you want to explore Jaipur to its full potential without heat and tanning and what not, then you should visit in winters around new year because most of the monuments have large areas directly exposed to the sun.
Of course not summers but its ok to roam aroind in the evening as its pleasant in the evening. October to March is the best time BTW for any Indian destination almost.
Hello Shraddha this is rishi I am from jaipur u can visit jaipur in monsoon too but the climate is bit humid and sometimes sunny too but u can see the lush greenery All over jaipur in monsoon season ...the next option is winter Dec end - Feb end This is the best season to visit here ...If u need further help feel free to ask