I visited this WHS in January 2012. It's a great base to visit the Jantar Mantar WHS and the inscribed Amber Fort which is only 11km away from Jaipur. Other nearby forts worth visiting with the one in Amer are the Jaigarh Fort and the Nahargarh Fort. 

The pink city was in dire need of restoration when I visited and pretty much everything except the Palace of the Winds/Hawa Mahal facade (photo) was crumbling although the structures are not that old! Jaipur is one of those places on the WH list which unjustifiably have separate WHS for specific buildings and as a historic centre/city but in my opinion it would make much more sense as 1 worthy WHS rather than having 2 which in such a case seems counterproductive. 

The Jaipur city palace is worth visiting if only for a good view of Diwan-e-Khas, Peacock gate and the entrance gate of Rajendra Pol. If you were to visit only one museum here, make sure to visit the Albert Hall Museum also known as the Government Central Museum, which is Rajasthan's oldest museum and a fine example of Indo-Saracenic architecture. The main highlight inside apart from the architecture, believe it or not, is a far-from-home Egyptian mummy!

Another highlight was the Water Palace or Jal Mahal in the middle of the Man Sagar Lake. The palace and the lake around it were renovated and enlarged in the 18th century by Maharaja Jai Singh II of Amber. When I visited the lake was full but apparently during the summer months the lake dries out! An old yet very interesting BBC documentary named Around the World in 80 Gardens (Episode 3) explains the palace's importance for water management and the unique features of Mughal gardens.