My best suggestion would be go to Udaipur. It's the most beautiful place according to me in Rajasthan. Although most places of Rajasthan are beautiful in it's own unique ways. Culture and History is all over Rajasthan. Jaipur is for Forts all around. 1000's of years of history. Udaipur is for beautiful scenery, forts, sunsets. If you want to see desert and forts you can go to Jodhpur and if you're a wildlife lover go to Ranthambore national park but i am not sure National park would be a good idea in monsoon. Choose any of these options they're all beautiful.