The princely state with pilgrimage sites of Palitana and Shatrunjaya Hills was:

Palitana
Bhavnagar
Junagadh
Wadhwan

The correct answer is: Junagadh.

Palitana and Shatrunjaya Hills are pilgrimage sites for Jains. They are located in the Junagadh district of Gujarat, India. Palitana is a town with about 30,000 inhabitants. It is located on the Shatrunjaya Hills, which are a group of hills with about 800 Jain temples. The temples are built on the slopes of the hills and are a popular pilgrimage destination for Jains.

Bhavnagar is a city with about 500,000 inhabitants. It is located on the Gulf of Kutch, in the Bhavnagar district of Gujarat, India. Bhavnagar was the capital of the princely state of Bhavnagar from 1729 to 1947.

Junagadh is a city with about 100,000 inhabitants. It is located on the coast of the Arabian Sea, in the Junagadh district of Gujarat, India. Junagadh was the capital of the princely state of Junagadh from 1540 to 1947.

Wadhwan is a town with about 20,000 inhabitants. It is located in the Surendranagar district of Gujarat, India. Wadhwan was the capital of the princely state of Wadhwan from 1752 to 1947.