Go blindly with Khandwa Haveli Jaipur! It's a heritage hotel and fits your budget!
Try Dera Rawatsar or Khatu Haveli. Also Nahargarh Haveli.
Clarks Amer or if you're looking for something more traditional, Chomu Palace Hotel
You can check out Alsisar Haveli
Themis mud house is the best and suitable option...