If you are passionate about palaces and forts , Jaipur is one of the best place to visit. Must visit places include Amber fort, City palace, Nahargarh fort. These are the prominent ones. Also there is a very lake in Jaipur - Man Sagar Lake. In the middle of the lake is the Jal Mahal. The place is a treat to watch at night.
1. for shopping go to johari bazar for beautiful bandhani dupattas/sareed/lehengas and the most exquisite silver jewellery (it is affordable too)
2. for a rajasthani village experience and dinner go to chowki dhani
3. for the most amazing rajasthani street food go to laxmi mishthan bhandar (eat kachoris, mirchi bada etc.). dont forget to buy methi and garlic khakra
4. for nightlife go to elephant-naila bagh palace. they have a disc, candle lit sitting area, good food and amazing crowd
5. for a little history go to jaigarh and amer forts and hawa mahal
6. a little insider tip (not many people know about this) - go to this restaurant 1135 AD which is in amer fort, it is a royal dining room inside the fort (i am assuming the maharaja owns it). this restaurant is royal in true sense (the paintings, chandeliers, cutlery etc). the food is better than average, but the experience is truly royal
Amber fort.. hawa Mahal .. jantar mantar.. and a lot..actually if you are on a budget travel, from Jaipur itself tourist buses are available for city roundoff