You can try this in sequence
first visit jaigarh fort then Amer fort.
then head towards nahargarh fort, spend the evening at rdb point.
watch late night show at Raj mandir.
next day visit hawa Mahal and jal Mahal. well you can see jal Mahal the previous day. there is no entry in jal Mahal, people watch it from 150 meters approx distance. can shop at bapu bazaar, go to Albert museums and City place. visit birla mandir and mooti dongri mandir.
You can book a safari which will take you to all the famous sites of Jaipur if you have a short span of time Or else you can travel on your own to
Birla temple Jantar mantar
1st thing you should visit, Jaipur City Palace followed by Amer Fort, Panna Menna ka Kund (A step well), Jal Mahal Palace, Hawa Mahal.
Do check out Gaitore ki Chhatriyan. It's a very beautiful place. Less crowded and Very quiet.
Pratika Gate is also a very beautiful spot near to Jaipur Airport. Very picturesque spot.
Go to Amer Fort at Morning time if you want to see/enjoy Elephant ride. Because it operates only from 7AM-11 AM.
You can do check out my recent blog which is on Jaipur. Hope it helps. Thanks!