You can always look for youth hostels to stay with like minded people with the budget friendly to your pockets. few hostels you can find in Jaipur are
Moustache
goStops
Zostel
The hosteler etc..
Highlights Sightseeing of City Palace, Hawa Mahal and Jantar Mantar. Enjoy Elephant ride at Amber Fort. Enjoy sound and light show in Jaipur. Take holy dip in the Pushkar Lake. Enjoy camel ride in Pushkar. Visit Brahma Temple and Rose Garden at Pushkar. Explore Dilwara Jain Temple at Mount Abu
If you have much low budget, You can cover all major places in a single day as well.. start from morning at 8-9 from hawa Mahal and then move to Amer fort than to its adjacent jaigarh fort, and lastly u can go to either nahargarh or jal Mahal by the evening. By this you will be able to cover almost all the major places in a single day and you might return the same night. This was my experience when I visited there the previous year.
If you are solo, you can try traveller hostels and you'll find them on Hostelworld website. The accommodation can be as cheap as 300₹ a night for a bed.
Things to see include :
Nahargadh(good for sunsets) Amer gadh
Panna Meena ka Kund
Galtaji Mata temple The fortification walls of Jaipur
The Tattoo cafe(For good pictures of the Hawa Mahal) Hawa Mahal
Jantar Mantar
City Palace Take a city tour in the double tier bus
You can book cabs and tuktuks(electric ones are cheaper) or someplaces even have a decent public transport facility like Amer gadh.Also don't forget Jal Mahal and Jaigarh