Trip to Rajasthan during New Years

Hello Everyone!! My brother and I are planning a 12-day trip to Rajasthan. We arrive in Jaipur at 30 and spend new years in Jaipur and then we go to Jodhpur, Udaipur and Jaisalmer. I am looking for suggestions as to what all can we cover in these 4 cities, we are looking for anything in general from hidden gems to food places to great chill spots to just enjoy the trip, please let us know of any recommendations! Shukriya!