I cant suggest you all the places, but what i would like to tell you is 4 days for jaipur only is too much . what you could do is plan a visit to ajmer or pushkar along.
For day 1 try covering Amar fort in half day then Jal mahal to hawa Mahal and jantar mantar.
for day 2 have breakfast in famous rawat ki kachori and then to city palace, after than go to the market if you want any souvenirs.
for day 3 try covering Jaigarh fort, Albert hall museum, birla mandir. For day 4 nahargarh fort, ram niwas garden, step well
4 days is too much. You can cover all the places in 2 days.
Don't forget to visit Patrika Gate.
City Palace, Hawa Mahal and Jal Mahal can be done in one day. Another half for Nahargarh fort. Amer fort is in ruins and it's light and sound show is also not that great. So u can avoid it.
On reaching jaipur, subject to time you reach you can finish your city sight seeing e.g. Hawa Mahal, Jantar Mantar, Birla Mandir, City Palace etc. On 2nd day visit Amer Fort, Jaigarh Fort, Nahargarh Fort and on way to Amer Jal Mahal. this will take your whole day as roaming around amer will 2-3 hrs and other forts will be 1-2 hrs each. You will be back in early evening in city, so do some shopping. On3rd Day Visit to Ajmer, Pushkar anad old pushkar.
On 4th Day if you are curious and interested visit Sariska Wild Life and Bhangarh Fort.