Jaipur City Palace is a nice visit, but I personally wouldn’t classify it as a “must-see.” The architecture is interesting, but it has more of a feel as a money-making experience rather than a historical tourist attraction, also – most rooms said no photography allowed.
The costume museum is interesting and worth a look. The Maharajah’s meeting room is also impressive. On the other hand, the paintings in the meeting room are quite impressive and (apparently) copyrighted – so you won’t see it in other places.
There are some shops outside of the palace where you can get some decent prices. Quality seemed to be good and the shop-keepers are a pleasant bunch.