Eating and drinking in Jaipur is a dream. This was the seat of power for the Kachwaha Rajputs, after all, so you can expect the cuisine to have influences of the richness that the need to satisfy royal palates brought out. Jaipur is also a very well-developed city, so there is no risk of lacking international or foreign cuisine restaurants for tourists getting homesick: from Italian to American food, there are certain places here that serve up dishes to fit the bill. When you are travelling in another country, though, what you really want to do is try out its local flavour. As such, you should aim to eat as many of the local specialities as you can.
An undisputed speciality of Jaipur cuisine is dal batti churma. This actually has three components: Dal is a variety of curried lentils, Batti is oven-baked wheat dumplings, and Churma is a kind of sweet that often has a component of flour with it too. The dumplings-lentils-sweet combination make for a most delightful, rustic dish… although you should be warned that most of the shops on the street bake the dumplings the traditional way: over a fire fuelled by cow dung. If this is likely to bother you (although it does not really affect the food in terms of smell or taste), then go to the cleaner establishments.
Then there is thali. Rajasthani thali is among the most popular versions of the dish. Thali is a well-known Indian dish that is served on a tray set with smaller bowls or dishes holding the many individual components that go into thali. Typically, the thali made in Rajasthan shall have roti, sabji or sookhi, dal, bati, rice, curd, a salad, and some chutney or pickles. A sweet is also part of the usual thali, especially as it is typical for Rajasthani people to eat sweets both before and after their meals: there is no strict “equivalent” for the Western concept of a dessert as the meal ender here.
Sweets are an important part of Jaipur cuisine, and you should not miss out on the chance to sample the popular ones, including ghewar (a special sweet that locals make during festivals that is sprinkled heavily with pistachios), kachori (a sort of fried dumpling or ball of flour that may be spicy as well as sweet) and jalebi (a kind of chewy pretzel coated with a syrupy substance on the exterior). These may be found all over the city as they are popular snacks, but the easiest way to find them is just to head to the road outside the Tripolia Gate of the City Palace, the Chaura Rasta. This is where you can find some of the best sweets in the city. For the special ghewar, try to come to the city during a festival such as Gangaur and head for the shops in Johri Bazaar.
As far as drinks go, cold lassi is par for the course here, especially as Jaipur is a very warm city. You can find it everywhere when looking for where to go eating and drinking in Jaipur. Be warned, by the way, that some places in the city that used to be of higher quality before have “gone over to the dark side”. For example, LMB at the Johri Bazaar used to be touted as an excellent and reasonably-priced place to go to in order to sample local cuisine: its popularity with tourists may have prompted the sharp spike in prices that many consider to be overpricing nowadays, though.