Jaipur is the biggest city and capital of Rajasthan, so you can arrive in whatever method you like. Unlike many other Rajasthani cities, the city center is car friendly, so feel free to pick whatever lodging you choose.
Day 1: Jaipur Fortresses
Although Jaisalmer is bigger because it contains a full town, Jaipur has the most to see in terms of forts as there are three of them: Amer (Amber), Nahargarh and Jaigahr Forts (plus the City Palace). Each fort has its own distinct pros and cons, but Amer is the largest complex I visited in all of Rajasthan. Note that Amer and Jaighar are further out of town as compared to Nahargarh.
Depending on where you are staying in town, the Gaitor Cenotaphs may be on your way to the outer palaces, and are worth a brief stop. much like other cenotaphs, there is nothing to see but the architecture of the pavillions, but it is collectively stunning.
Day 2: Pink City
Jaipur is known as the pink city, and if you go the city centre, you'll find it lives up to its moniker. Pink sights in the city center include the tripolia Bazaar (overpriced but easily accessible), the City Palace, and the Hawa Mahal, which is really just a wing of the City Palace. The astrological park, jantar Mantar, is also a unique place worth visiting as the odd structures are unique in their uses for astrology (even if, like me, you don't believe in it).
Day 3: Hanuman Temple
If you didn't see any monkeys in Udaipur, worry no, as this temple will scratch that itch. Just be careful with your belongings. The temple complex actually hosts numerous other structrures, but to be honest, the monkeys are the most memorable part. I finished this day off by visiting Nahargarh Fort, as it is the odd one out geographically.
As the capital of Rajasthan, Jaipur is very well connected in terms of transit out of the city. It is also reasonably close to Delhi - a Taxi ride is about 4 hours, and the price is not prohibitively high if you are in a grup, or want the added comfort. As I was alone, I took one of the numerous daily trains to Delhi.