Totally do-able! I went around Jaipur and did a superfast sightseeing in a day's time. Of course l had to prioritise! Two days would have been more comfortable, though. Must Do's: 1. Amer Fort (If uou can manage to include the light n sound show in the eve as well, nothing like it!)
2. City Palace - is a sprawling museum. Can take up a lot of time if museums are your thing. So, plan accordingly.
3. Jal Mahal - I had to see it from a distance but 2 days is good enough time to visit this one.
4. Hawa Mahal - The rooftop cafe right across the street is a great viewing point. And right below is the market area for some memento shopping. Try out local Rajasthani cuisine - dal bati churma and ghewar in case you haven't ever had it earlier. Also, pretty much every place in Jaipur is easily reachable by local commute. So that's easy on the pocket. Hope this helps!
Get a place in Zostel. It's the best place if you are backpacking. Plus it's in the heart of the city. Connect to anyplace from here. So start your day from visiting Amber Palace. It is stunning. don't miss the museum which is at the entrance and the top is Nahargarh Fort. it has the wonderful view of the whole Jaipur. Then on your way back have a look at Jal Mahal. Unfortunately you can only get a long distance view. Then find amazing food places around the zostel or Hawa Mahal. or roof top cafes opposite to HawA mahal. for a beautiful sunset. the next day start with city palace, Hawa Mahal, Jantar Mantar observatory and finish the day off with Pink city bazzar shopping.
1.City Palace 2.Jantar Mantar 3.Hawamahal
4.Isarlat Day 2
1.Nahrghra fort 2.Amber palace
3.Galtaji temple(Monkey Temple)
4.Gaitor ki chatriya
5.Jal Mahal Day 3 1.Albert Hall
Yes, you can visit most of the touristy places in two days stay in Jaipur. The places I visited are - Jantar Mantar, City Palace, Amber Fort and palace (also check out light and sound show here), Panna Meena ka Kund, Hawa Mahal, Johri Bazar and Bapu Bazar are good for shopping as well.
Hire a sightseeing taxi and 2 days are enough to visit Jaipur with comfort. It's possible because most of the iconic places of Jaipur are nearby to each other like Jantar Mantar, Govind Devji Temple, City Palace, Hawa Mahal, Albert Hall museum, Gatore ki Chhatriyan, Amber Palace, Jagat Shiromani Temple, Panna Meena Baori, Jal Mahal, Kanak Vrindavan, Nahargarh Palace, Jaigarh Fort, Nahargarh Biosphere reserve, Elephant Village, etc. Other than these, you can visit Moti Dungri Mandir, Birla Mandir, Sisodiya Rani Bagh, Galta Temple (Monkey Valley), Choolgiri Hills, etc.
You may even choose places wherever you want to visit in Jaipur.
Two days is sufficient for jaipur first day you go nahargarh fort to see best sunrise view then you go jaigarh fort to see biggest canon- Jaivana canon then go amer fort then go alber hall museum at night and take best local food at masala chowk jaipur.
you go local market city palace jantar mantar govind dev ji temple then you can go world trade park and gourav tower. after this you can go to patrika gate. At evening you chokhi dhani for best rajasthani food and to see local culture and rajasthani folk dance... Thank you Warm Regards Manuj Pareek