Jaipur
This was my second visit to Jaipur. I had previously visited in 2009, at the end of multi-city India tour. That first trip hadn't left a strong impression on me. This time, Jaipur, was the start of a multi-city Rajasthan tour.
Jaipur has several highlights. Jantar Mantar is an 18th astrological observatory and is an impressive set of structures. It was particularly helpful to have a knowledgeable guide who explained how the instruments worked. My favorite experience in Jaipur was the City Palace tour. We took the Royal Splendour tour which at first seemed overpriced at $45 USD. However, it was worth the money. The tour provides a private guide and gives one access to some gorgeous rooms in the palace. The tour is very uncrowded and we had time in each of the rooms to ourselves.
If you only have time to visit one city in Rajasthan, Jaipur should be it.