Udaipur and jaisalmer becuase udaipur has much visiting places and jaisalmer is very beautiful becuase of Thar desert and Forts.
Night at Thar desert is a wonderful experience , and please take jacket with you at night to escape from cold.
I have lived in Rajasthan all my life, so I'll try to answer your question in every honest way.
Udaipur is one of the best locations for monsoons. It is green, it is lush and it is full of beauty. The places in the city itself, i.e. the city palace, the lakes, the markets- hathipole and babu bazar are both equally full of handicrafts and culture. The sajjangarh fort and biological park are a beauty and give a view that makes you think whether even you're in Rajasthan or Himachal. Also the kala kendra displays some beautiful folk dances and culture of Rajasthan.
Outside the city, you can go to Fort Kumbhalgarh which is a phenomenon in itself and the most beautiful fort I have ever seen. It has the 2nd longest wall in the world, yes after the great wall of China.
The night life in Udaipur is crazy and full of life and fun. The city is also safe.
It is a lifetime experience. If you want to read more about Udaipur and Kumbhalgarh, you can read it in my trips and blogs.
So Udaipur is a big yes. Carry a windcheater or raincoat, you'll need it trust me.
The second ideal choice would be Jaisalmer. The 'sam' is something you will not find in any other place in India that you'll visit. You can go on camel safari in the desert all day and it would like an adventure sport climbing all the sand dunes and at night you can sit and chill with the folk culture and bonfire.
Carry some warm clothes for the night. It is beautiful.
Jodhpur is last but not the least. I have a special place for that city since it is my 'nanihal'. So I know every nook and corner of that place. If you have a chance, do visit Jodhpur too. It has a magnificent fort, Mehrangarh and you'll need a while day for that. Also, 'stepwell' bawdi from which little boys and children jump into water, it is just like cliff diving. There are numerous other places both to have fun at and eat and dine.